My rule of thumb: nicknames are the place to let creativity, whimsy, and affection loose. Nns don't have to scientifically emerge from the sounds of the formal name. So
Francis, nn
Finn, makes perfect sense to me. Then again
Francis, nn Hoppity Hop, makes sense as well. :0)
When I first read your heading I thought of suggesting
Fitz (= son) as a nn for
Francis. But
Finn is just as cute.