I recently saw this film and could have sworn that the songs were sung by Edith Piaf herself. BUT in the credits at the end was one entry: Jil Aigrot ...Edith Piaf (singing voice).
I can't believe I didn't hear Piaf herself singing and wonder if the credit referred to when Piaf was depicted as a child when of course there would be no recordings of her.
I'm sure I read in a review that the adult voice WAS Piaf's and the actress had to spend a lot of time learning to lipsynch so perfectly. So you're probably right about the child thing.