Its a pretty old jazz standard by Nat King: https://en.wikipedia.org/wiki/Nature_Boy

There are tons of versions and variations of it

It does in fact show up in Moulin Rouge: https://www.youtube.com/watch?v=ekCvBztYs_A

It's Nature Boy, originally recorded by Nat King Cole. https://www.youtube.com/watch?v=Iq0XJCJ1Srw - it's one of those songs that's been recorded by a ton of artists from that era. I personally heard Ella Fitzgerald's version first.