The relationships of Beast/Prince Adam.
The Beast first meets Belle when the latter tried to free her father Maurice whom the Beast had previously imprisoned him for trespassing into his castle, where Belle was terrified of the way he looked in the light and took and instant dislike towards him due to his abusive nature and unstable temper. Astonished by Belle's selflessness to take over her father's place as Beast's prisoner, Beast ultimately takes Belle as his prisoner, under the further condition that she remains in the castle forever.
The Beast eventually decided to give her an actual room other than the dungeon cell (both at Lumiere's suggestion and due to feeling some guilt at Belle's sadness from his prior actions). He further warns Belle not to go into his chamber, the West Wing, although he gave her expressed permission to visit the other areas of the castle. When all of the Beast's servants are aware the Belle could be the one that could break the spell, Beast often struggles to treat Belle nicely despite his servants' advice, often ending badly with them fighting and the Beast angrily yelling his head off at Belle, which he immediately feels regretful of. Once the Beast Beast rescues Belle from a pack of wolves (at the cost of injuring himself and passing out in the snow), Belle starts tending his wounds, but the two then enter another brief argument about who is at fault, with Belle effectively winning the argument with telling off the Beast for his unstable temper. As Belle, having conquered the Beast's ferocious temper, continues to tend to his injuries, she thanks him for saving her life, to which the Beast, realizing the deed he has just done while noticing her kindness, starts feeling good inside himself.
Shortly after the Beast rescues Belle from a pack of wolves, Beast slowly learns to treat Belle nicely, although his hatred towards Christmas due to the painful memories it evokes puts an abusive strain in his relationship with her. Eventually, the Beast then finally overcomes his hatred of Christmas when Belle gifts him a storybook centering on him and therefore gives Belle the Christmas she has always wanted.
As the result of the Beast treating Belle much better than before (including gifting her the entire castle library), and the mutual bonds shared between each other, the Beast starts developing romantic feelings for Belle, even though Belle hasn't reciprocated his feelings yet. In his final act of selfless sacrifice, after sharing a ballroom dance with Belle, the Beast finally releases Belle in order for her to tend to her ailing father, despite that it would greatly upset him and would prevent the curse from being broken, because he indeed loves her.
After a epic battle between the Beast and his jealous rival Gaston which nearly costs the former's life, the Beast, whom was about to die due to his stab injuries from Gaston, confesses his final words, telling Belle who had recently returned to the castle on how grateful he is to have a chance at seeing her one last time before succumbing to his wounds. As Belle mourns for his death, she finally admits her love for him, mere seconds before the last petal falls from the enchanted rose, which enabled the spell to be broken, and the Beast to be resurrected back to life as a human Prince. By the end of the film, both Belle and the Prince happily dancing in the ballroom, surrounded by his servants and her father watching the two happily.
Friends and Allies
Lumiere is one of the Beast's servants where he serves as the castle's maître d'. Lumiere is loyal to the Beast, but fears his master's hot temper where he was a tendency to disobey his master's orders. Despite this, the Beast is shown to have a close relationship with Lumiere than with any of the servants.
When the Beast discovered Maurice in the castle one day, Lumiere tried to explain that he allowed Maurice inside as the latter was lost and cold, but the Beast roared in Lumiere's face and proceeded to throw Maurice in the dungeon for "trespassing." After Belle arrived to take her father's place, the Beast seemingly rejected Lumiere's suggestion of having Belle stay in a more comfortable room, but took Lumiere's advice after seeing how sad Belle was over not being able to say good-bye to her father. As the Beast took Belle to her room, he was advised by Lumiere to speak to Belle and make her feel welcome.
After Belle refused to have dinner with him, the Beast ordered Lumiere and the other servants to not serve her dinner, but Lumiere disobeys his orders and serves Belle a meal. Later, when the Beast decided to do something for Belle, he took Lumiere's suggestion to show the castle's enormous library as Belle loved to read books where he then gave the library to Belle as a gift.
As the Beast's love for Belle continued to grow, he was given confidence by Lumiere to admit his feelings to Belle. While the Beast shared a romantic waltz with Belle, Lumiere proudly watched his master dance with the girl he's grown to love. When the Beast released Belle so she aid her father, Lumiere became depressed, thinking with Belle gone, there would be no chance to break the spell and become human again. After the Beast's fight with Gaston, Lumiere came to his master's aid and watched as Belle confessed her love for him, thus breaking the spell. Prince Adam shared an embrace with Lumiere and was happily watched by the latter while sharing another waltz with Belle.
Cogsworth is one of the Beast's servants where he is actually the majordomo of the Beast's castle. Cogsworth feared his master's temper that he was willing to obey his orders, out of fear of being punished by his master. When Maurice arrived at the castle, seeking shelter, Cogsworth tried to get the old man out, fearing what his master will do to him, only to watch the Beast wrongfully throw Maurice in the dungeon for "trespassing."
When Belle took her father, Maurice's place and refused to have dinner with the Beast, Cogsworth obeyed his master's orders to not serve her a meal, but relented at Lumiere's urging. Cogsworth then helped his master fall in love with Belle where he gave him suggestions on what kind of gifts to her. When the Beast released Belle to tend to her sick father, Cogsworth was shocked to hear this and became depressed, believing with Belle gone, there would be no chance to break the spell.
After the Beast's fight with Gaston, Cogsworth came to his master's aid and watched as Belle confessed her love for him, thus breaking the spell. Prince Adam happily shared an embrace with Cogsworth who later watched him and Belle share a romantic waltz together.
Mrs. Potts is one of the Beast's servants where she is the head housekeeper of Beast's castle. Though Mrs. Potts feared her master's violent outbursts, her stern attitude also had a strong effect on the Beast, who appears to respect his head housekeeper the most out of all his servants—he has even been shown to occasionally snap out of his violent tantrums when she confronts him on his behavior.
After Belle sacrificed her freedom to take her father's place, Mrs. Potts advised the Beast to be patient with Belle and tried to help him be a gentleman. When the Beast and Belle formed a friendship and started to develop feelings for each other, Mrs. Potts helped them fall in love and sang a romantic song during their ballroom waltz. However, when the Beast set Belle free so she could aid her sick father, Mrs. Potts was shocked while sadly confirming that the Beast has finally learned to love and with Belle gone, there would be no chance to break the spell.
After the Beast's fight with Gaston, Mrs. Potts came to her master's aid and cried when he died of his injuries. However, Belle managed to confess her love for the Beast, breaking the spell and reviving him. Prince Adam shared an embrace with Mrs. Potts who watched him and Belle share another waltz while assuring her son that Prince Adam and Belle will live happily ever after.
When Maurice had come to his castle seeking shelter after getting lost in the woods and being chased wolves, the Beast, unlike his servants, did not warmly welcome Maurice and offer hospitality. Instead, the Beast was angry that Maurice was in castle and accused the old man of trespassing. The Beast's accusations and rage frightened Maurice where the Beast mistakenly assumes that Maurice had come to stare at his monstrous appearance, causing him to wrongly locked Maurice in his dungeon.
When Maurice's daughter Belle arrives and pleas for her father to be released, the Beast refused to set Maurice free as he was still angry over the old man "trespassing" into his property. However, when Belle offered to take Maurice's place, the Beast agreed and released Maurice, but instead of letting him say good-bye to Belle, he immediately threw Maurice into a spider-like carriage to return him to his village while telling him that Belle was no longer his concern.
As the Beast fell in love with Belle, he allowed her to see her father through the magic mirror. When the Beast saw how distraught Belle was to see her father on the verge of dying, the Beast, who had changed for the better, decided to release Belle so she can release her father as a way to make amends for earlier harsh actions on Maurice.
After the spell was broken where the Beast was turned back into his human form, he was happily watched by Maurice as he shared a waltz with Belle. It is also indicated the Beast, or Prince Adam, had fully made amends with Maurice and was accepted as the latter's son-in-law due to his marriage to Belle.
When Belle revealed the Beast's existence to the villagers, in order to save her father, Maurice from being thrown into a mental asylum, Gaston was shocked as he did not believe Maurice's claims about a beast living in a castle. However, when Belle described the Beast as "kind and gentle," Gaston who wanted to marry Belle, become increasingly jealous upon realizing Belle was in love with Beast instead of him. This motivated Gaston in forming a mob so he can storm the castle and kill the Beast so he can have Belle all to himself.
When Gaston arrived at the castle and found the Beast in the West Wing, the Beast allowed Gaston to attack him as he lost his will to live after Belle's departure. However, when Belle returned to save him from Gaston, the Beast regained his inner strength and fought back against Gaston. Gaston taunted the Beast over his love for Belle and claimed that Belle was his property, which caused the Beast to angrily head-butt him in the chest. The Beast then proceeded to drop Gaston over the edge of the castle, as punishment for his actions. The Beast ignored Gaston's pleas for mercy, but upon realizing that Gaston is nothing than a reflection of his former self, the Beast reluctantly spared Gaston and ordered him to leave the castle and never return.
As the Beast embraced Belle, he stabbed by Gaston who intended to make one last attempt to kill him and have Belle for himself. However, Gaston fell to his death and although the Beast died of his injuries, he was soon revived after Belle managed to confess her love for him, breaking the spell and making Gaston's attempts end up in vain after the latter's death.
Forte is one of the Beast's servants where he is the former music conductor of Beast's castle. He initially appeared to the Beast as his "best friend", but he was actually manipulating him because he wanted to both remain as a pipe organ and sought some attention. However, they won't become flat-out sworn enemies until Belle enters the Beast's life, as this attitude is only displayed because he is quite afraid to fade in the background, afraid that he will be forgotten.
Unlike his master and the rest of the other servants where they hated their cursed forms and all worked hard to undo the curse, Forte accepts his new cursed form and this is what drove him into madness. As Beasts reforms and learns to overcome his hatred towards Christmas over the course of the film, Forte's frustrations continues to reach breaking point, because of his paranoia that he'd lose his newfound ability in music he gained in his enchanted form once he becomes human again and Beast would forget him in favor of Belle. Once Beast finally overcomes his hatred for Christmas in order to give Belle the Christmas she has always wanted, that was the last straw for Forte: In a last crazed attempt to prevent them from breaking the spell, Forte decided to destroy the whole castle and used the strongest musical scales of Beethoven's 5th, because, as he put it, "they can't fall in love if they're dead!"
The Beast, finally had enough of Forte's treachery, decides to destroy Forte once and for all by ripping keyboard away from Forte (courtesy of Fife who had just turned against Forte at the same time), hence effectively 'kills' Forte and he crashed to the ground, destroyed. Though he knew that Forte had villainous designs, the Beast mourned the death of his best friend with Belle comforting him.