Welcome to the boards! Good question.
FFC believed doing a sequel on The Godfather was a: "Sure way to fail.", he thought about it and decided to make GFII. The same thing was the case with GFIII, FFC absolutely wanted Michael to be the main character in GFIII, it would be a completely different GF, because Michael was different. He was gonna make a movie about Michael thinking about his sins, it was so different that FFC diden't even wanted the movie to be called GFIII, the executives of Paramount wanted the movie to be called: "The Godfather Part III.", FFC diden't agreed with this, he wanted it to be called somehing like: "The Dead Of Michael Corleone.". FFC diden't have that kind of power to decide what was gonna be the movie's name, so it was gonna be "The Godfather Part III.".