In French, accents determine how the name is pronouced. If I were to use a French (or Italian/Bulgarian/Japanese/etc.) name, I'd make sure I spelt it the original way. Amelie (without the accent) is a perfectly legit name - only it's German, not French!
And, btw, the pronunciation of Amélie is actually closer to [ah-meh-LEE]. The sound "é" doesn't exist in English, but it certainly doesn't sound like "ay" ;)