As a Francesca myself, I wholeheartedly put a vote forward for it. I've always been 'Faya' at home (God knows where it came from) but I've always loved my full name. I quite like Fran too, and was frankie occasionally as a child which my parents liked (but I didn't).
I'm slightly biased, but Madeleine especially with the nn maddie is quite common these days due to it also being the nn for Maddison.