The section of soundtrack in 'Amelie' actually features a sample of Billie Holliday's original 'God Bless The Child', and the soundtrack composer is Yann Tiersen, so I imagine he is responsible for the piece of music in which that sample is contained.
Alex Gopher has used a sample from God bless the child on the track 'the child'. This was released as a single as well as being available on the album 'me, my baby and I' on source records. I don't know if this appeared on the film amelie though.