Phantom of the Opera, A Monster in Paris, Hunchback of Notre Dame...All of them take cues from the original La Belle et la Bete story, and even share the same setting of France. Do you guys think the setting in France is an important aspect of the story?

The Hunchback of Notre Dame has to be in France because that's where both the writer and Notre dame are.

I'm... a little confused by the question. A lot of the examples you listed don't seem like they were directly inspired by the Beauty and the Beast fairy tale.

The Phantom of the Opera (Le Fantôme de l'Opéra) was a novel written by Gaston Leroux, inspired by the real life Paris Opera House. I went and visited it once. It's a beautiful building, and really does have watery canals under it. Apparently the magnificent architecture inspired the story.

Likewise, The Hunchback of Notre Dame (actually titled Notre-Dame de Paris) was a novel written by Victor Hugo, which was in turn inspired by and created to increase appreciation for the breathtaking architecture of the Notre Dame cathedral.

I don't know anything about A Monster In Paris, so I can't comment.

Maybe there is something about the French culture that inspires so many "beast loves the beauty" stories, but I wouldn't go so far as to say they were directly homages to Marie Leprince de Beaumont's story, or that the authors chose the French setting just because she did, because they themselves were also French and picked their French settings for their own reasons.