Biologically humans have either XX or XY chromosomes XX's are female XY are male. It's the Y that makes males male. You get 50% of you DNA from your mother and 50% from your father. However because only males have a Y the Y-DNA test can only trace male to male to male.
For a mixed gender test (which FTDNA calls a Family Finder test) you are matching a percentage of your genes vs others. So for your cousin he will match about 50% with his father, 25% with his father's father, 12.5% with his father's father's father etc. However also across a female line so 50% with his mother, 25% with his mothers mother, 12.5% with his mother's mother's mother. Also across mixed genders so 50% father, 25% father's mother, 12.5% father's mother's father. etc.
Thus after 3 generations we are down to only a maximum of 12.5% shared DNA, after 4 generations down to 6.25% after 5 generations down to 3.125% etc. Now that's still hundreds of millions of DNA pairs to match on so its a huge match. However a few more generations and the percentages shrink to very dodgy chance of a match. So after 8 generations say we have only a 0.39% chance of a match. Thus FTDNA say the family Finder test is good for a match up to around 5 generations back. It sounds like your Frank will be within 5 generations of your cousin so its likely a match may be possible.