I love
Francesca, personally. I think it's beautiful and at least where I live it's very uncommon. Good choice. :-) I'd say stick with
Francesca instead of changing it to Frachesca.
This website lists
Franca as a contracted form of
Francesca, and personally I think it would make a cute nickname. I don't like
Fran myself, either.
But if you don't like any possible nicknames for it, I still think it's very possible to just have your girl go by
Francesca. I know Elizabeths, Catherines, Bethanys, Andrews, and so on that use their full names and never a nickname. It's very possible to use her full name and, if that's what she prefers when she's old enough to decide for herself, other people will likely use it to instead of a nickname. With a name this uncommon, too, I don't think there's a nickname that people will automatically assume (like
Liz for
Elizabeth) and they'll be less likely to use it without her specifically telling them to.
I say go for it. :-) It's a beautiful name. By the way, do you have ideas for a middle name? Just curious!