I like
Parthenope,
Parthenia not so much but it's fine, maybe more as as a middle name.
Fae for
Frances is a bit of a stretch (incidentally, I much prefer
Fay as a spelling).
Frances is beautiful and it doens't need any nicknames, if you dislike
Franny. WDTO
Fran, by the way? Sometimes people who can't pronounce my full name properly call me that?