I think [name_f]Francesca[/name_f] sounds better with an Italian-sounding first name.
In addition to the names you said you like, how about…
[name_f]Carina[/name_f] (nn [name_f]Cari[/name_f] or [name_f]Ina[/name_f]?)
[name_f]Caterina[/name_f] (nn [name_f]Cat[/name_f] or [name_f]Ina[/name_f]?)
[name_f]Albertina[/name_f] (nn [name_f]Tina[/name_f] or [name_f]Alba[/name_f]?)
[name_f]Rosa[/name_f] (nn [name_f]Ro[/name_f]? Though no nn needed)
[name_f]Rosaria[/name_f] (nn [name_f]Rosie[/name_f], [name_f]Rosa[/name_f], or [name_f]Aria[/name_f]?)
[name_f]Rosalia[/name_f] (nn [name_f]Rosie[/name_f], [name_f]Rosa[/name_f], or [name_f]Lia[/name_f] (prn [name_f]Leah[/name_f])?)
[name_f]Gia[/name_f] (nn [name_f]Gigi[/name_f]?)
[name_f]Giada[/name_f] (nn [name_f]Gia[/name_f] or [name_f]Gigi[/name_f]?)
[name_f]Gianna[/name_f] (nn [name_f]Gia[/name_f] or [name_f]Gigi[/name_f]?)
[name_f]Giovanna[/name_f] (nn [name_f]Gia[/name_f] or [name_f]Gigi[/name_f]?)
[name_f]Giulia[/name_f] (nn Giuli, [name_f]Gigi[/name_f], or [name_f]Gia[/name_f]?)
[name_f]Giuliana[/name_f] (nn [name_f]Giulia[/name_f], Giuli, [name_f]Gigi[/name_f], or [name_f]Gia[/name_f]?)
[name_f]Adriana[/name_f] (nn [name_f]Ade[/name_f], [name_f]Ada[/name_f], or [name_f]Ana[/name_f]?)
[name_f]Tatiana[/name_f] (nn [name_f]Tati[/name_f], [name_f]Tia[/name_f], or [name_f]Ana[/name_f]?)
[name_f]Arianna[/name_f] (nn [name_f]Aria[/name_f], [name_f]Ari[/name_f], or [name_f]Ana[/name_f]?)
[name_f]Emiliana[/name_f] (nn [name_f]Emmy[/name_f], [name_f]Emma[/name_f], or [name_f]Lia[/name_f] (prn [name_f]Leah[/name_f])?)
[name_f]Antonia[/name_f] (nn [name_f]Tonia[/name_f], [name_f]Toni[/name_f], or [name_f]Ane[/name_f]?)
[name_f]Cosima[/name_f] (nn [name_f]Mia[/name_f], Sia, or [name_f]Coco[/name_f]?)
[name_f]Nicoletta[/name_f] (nn [name_f]Etta[/name_f] or [name_f]Nico[/name_f]?)
[name_f]Elisabetta[/name_f] (nn [name_f]Elle[/name_f], [name_f]Lisa[/name_f], or [name_f]Bette[/name_f]?)
[name_f]Eleonora[/name_f] (nn [name_f]Elena[/name_f] or [name_f]Nora[/name_f]?)
[name_f]Vittoria[/name_f] (nn [name_f]Tori[/name_f] or [name_f]Vita[/name_f]?)
Of these, my favorite combination are probably [name_f]Gianna[/name_f]/[name_f]Gia[/name_f] [name_f]Francesca[/name_f] and [name_f]Giulia[/name_f]/[name_f]Giuliana[/name_f] [name_f]Francesca[/name_f].
I think for some names making [name_f]Francesca[/name_f] the first name sounds better, for others it needs to be the opposite, and some could go either way. [name_f]Francesca[/name_f] [name_f]Vittoria[/name_f]; [name_f]Francesca[/name_f] [name_f]Antonia[/name_f]; [name_f]Francesca[/name_f] [name_f]Elisabetta[/name_f] or [name_f]Elisabetta[/name_f] [name_f]Francesca[/name_f]; [name_f]Francesca[/name_f] [name_f]Arianna[/name_f] or [name_f]Arianna[/name_f] [name_f]Francesca[/name_f]; [name_f]Adriana[/name_f] [name_f]Francesca[/name_f]; [name_f]Tatiana[/name_f] [name_f]Francesca[/name_f]; and [name_f]Rosa[/name_f] [name_f]Francesca[/name_f] are also nice combinations.
Of the first names you said you liked, I like [name_f]Sofia[/name_f] [name_f]Francesca[/name_f]. But at the same time, both [name_f]Sophia[/name_f] and [name_f]Sofia[/name_f] are pretty popular. I know that matters to some people; don’t know whether it matters to you.