I would think there would have been a clause in the contract that allowed all the rights to the Godfather to revert back to the Puzo estate if Paramount didn't make any more Godfather movies. This happens with superhero movies all the time -- studios make them so the rights don't revert back to Marvel Studios.

Since Paramount hasn't made a Godfather movie in 22 years, they don't have much of a case, IMO.