I like
Frances; I prefer
Francis for a male but I would keep the full form and not use
Frank, though I don't mind it.
Frank, short for
Franklin, would be fine.
Frances for a girl shouldn't need a nn, but the only one I've heard has been
Fran, to rhyme with Fan, although
Frances has a long A sound.
Frances Deborah MaryFrances Margaret ClareFrances Alison May