I love
Madeleine, truth be told. It's a beautiful name.
As for the diminutive, it really depends on if you stick with calling her
Madeleine. My mother always called me Becki, so that (or
Rebecca in formal situations) was my preference even when others tried calling me
Becca. My neighbor goes by
Matthew even informally because his father is
Matt. People will get used to using whatever the child likes to be called, and in their early years it will probably be whatever you call them.
“Fairy tales are more than true; not because they tell us that dragons exist, but because they tell us that dragons can be beaten.”
― Neil Gaiman