NARRATOR: Ashamed of his monstrous form, the Beast concealed himself inside his castle, with a magic mirror as his only window to the outside world.
Shame is a powerful tool in terms of creating the Beast's exile. He's perfectly capable of leaving the castle; he just refuses to. In so doing, he ensures his own doom since he's not exactly going to meet a lot of girls that way.
BELLE: Every morning just the same /
As the morning that we came /
To this poor provincial town.
This is a very telling line: Belle isn't native to this village. She arrived there with her father sometime in the past, but recently enough for her to remember. That makes her an exile by default and very subtly connects her to the Beast, who's also exiled.
TOWNSPEOPLE: It's a pity and a sin /
She doesn't quite fit in.
No kidding. It feels like she's been an outsider in her village from the beginning. In that sense, Belle's spiritual exile links her to the Beast even before the two of them meet.
BEAST: She's no longer your concern! Take him to the village!
As the Beast throws Maurice out of the castle, we come to a funky realization. The old man is just as exiled when he gets back to town as he was locked up in the Beast's tower. "Exile" in this case doesn't mean a physical place so much as being separated from someone you love. (In this case, it's Belle, who's taking his place.)
BELLE: Promise or no promise, I can't stay here another minute!
The incident with the wolves shows us the very practical dangers of exile. We really mean it when we call it the Murder Forest; leaving without permission definitely carries its share of risks. Contrast this with the Beast, who's been perfectly capable of leaving whenever he wanted.
GASTON: Of course, old man! We'll show you out!
Maurice's exile from the community is less dire than the Beast's, in that he's still in the village among the community. But, for all practical purposes, it's no different. They've locked him out and have no interest in lending a hand.
TOWNSPEOPLE: We don't like what we don't / Understand; in fact, it scares us /
And this monster is mysterious at least.
A nice demonstration of tolerance and compassion from the local angry mob. Stay classy, yokels.
LUMIERE: Sacre bleu! Invaders!
We're assuming that the town itself lies within the Beast's domain, meaning that the peasants should be beholden to him. Heck, some of his enchanted servants may have come from the village. Instead, Lumiere calls them "invaders," suggesting that they are not a part of his good-buddy brigade anymore.
BELLE: Please! Please! Please don't leave me! I love you…
The threat of exile doesn't diminish just because Gaston is dead. If the Beast dies, he leaves Belle unable to reach him, still shut off from a sense of belonging and apt to stay that way for the rest of her life. Glad she got in that "I love you" just in time.