http://www.aniboom.com/video/258/The-Piano/

The song is so familiar to me, is it from a movie I may have seen? Or is it a well-known piece?

I have the feeling it's from a movie I saw. If anyone knows, could you tell me? And if it's a song I could get from somewhere, what's the title?

Amelie the movie

Good call Twist. It was also used on that BBC "The Apprentice" spinoff show "The Restaurant"