In "The Kid Stays In The Picture" (autobiography of Robert Evans, who helped produce The Godfather) he says that Coppola did not initially want to make the film and had to be convinced. He also forced Coppola to make The Godfather longer and pushed back release to do so, in order to tell the fuller story of the family.
I watched the documentary adaptation of his book and it is quite interesting, Paramount helped to pioneer the practice of helping to foster good books for film adaptation - The Godfather being the most notable example.
Coppola also said tha he did not want to direct the second movie of the saga, so he asked three conditions: to have no interference, a lot of money and to name the the movie the Godfather part 2. Strangely the third condition was the one which was most difficult to satisfy.
Of those three conditions it’s the one that sounds the most like it’s just there to give the studio a chance of getting the last word in a negotiation.
I watched the documentary adaptation of his book and it is quite interesting, Paramount helped to pioneer the practice of helping to foster good books for film adaptation - The Godfather being the most notable example.