i think its a great idea but if your partner doesn't like it then why not find a name which is the same as frank just a different version of it? here are some suggestions:
Francis
Franklin
Franco
Franz
Frankie
Famous bearers of this name include Frank Lampard (footballer), Frank Bruno (boxer), Frank Sinatra (singer) and Frank Zappa (musician).
my son is called James he was called after my brother, my uncle my grandfather, my greatgrandfather my greatgreat and so on lol.....
all my son's middle names are family names also, i wanted to call him after my grandfather who died when i was four who was called Andrew but maybe in the future if there is another son.... we'll see....
if we have a daughter in the future we're going to call her Elizabeth after my OH's grandmother who is almost 100.... i am hoping she'll meet elizabeth if we were get pregnant, my OH's grandfathers name is Jack (john really) and considered using Jack if we have a boy but not sure as my partners father died 5years ago so really want to name our son if we have one William after him.
we'll see as we're battling infertility atm.