I think it works.
But, Amelie is gorgeous while Millie kinda cheapens its beauty. I don't feel that way about other names with Millie has a potential nickname. Maybe just because this name is French and sounds so lovely when said aloud? I wouldn't want to shorten it.
All of this!
I agree as well! Amelie is too short for a nickname, too - it just feels like you're trying to use two good names. It isn't necessary, and Amelie is too beautiful to be shortened to Millie. I love Millie, but I think Amelie is too classy for it.