I know a Pierre and an Amelie and I have an Amelia 
I hate it when a name is described as "common in both senses of the word"
Despite all the hype I am yet to meet another Amelia or Millie and don't care when I do. It's a beautiful name for a beautiful little girl.
I was worried about how popular a name it was, but I can honestly say I have no regrets. I'm so glad I didn't go with our less popular second choice.
If you want Amelie go for it, you could pick a less well known name that has a surge in popularity the following year anyway.