Oh wait, you're right, Be Our Guest is in 4/4, sorry my bad.
Yes Jesse! Everytime I hear "Part of Your World" I think about Audrey's "Somewhere That's Green" too! I'm glad I'm not the only one who feels that way. I am a fan of his stuff, too, caveats aside.
So yeah, Gn2Dnlnd is right, I think. Granted the actual written melody in score for Les Poissons is very different from the sung quasi-improvisation, I guess it's close enough to Be Our Guest, but I would stop short of saying they are identical.