I like Francesca.
The only Francesca I know in the UK is called Cesca... Not sure if you'd be ok with that shortening...?
Daisy is lovey. But it could still be shortened. Or she could have a nickname just for the sake of having one...
DeeDee, Dais, Day, Sissi, Cee-Cee, Zee or maybe even Dupsie? Or something not even related to the name?