The tragedy of the Godfather is the fall of Micheal. The beginning scene is the mortician coming to the Don after the American justice system fails. The theme of the movies is set their. The conflict between the old ways of the mafia and the modern way of the citizen.
Micheal enlisting in the army is his rejection of the old way of family above all and his embrace of his citizenship and its duties. When he comes back he plans just to visit and then go marry the outsider, leave the family, and be a regular american. The Don wants this too because he knows Micheal is the smart one in the family.
However, the recklessness of Sonny gets his father attacks and Micheal then embraces the old ways of mafia and family life. He kills McCloskey, the symbol of the government, and leaves Kay. He eventually marries a Sicilian girl, symbolizing his full embrace of that lifestyle. At the end the ethos of family above all leads to the death of Sonny, the murder of Fredo, and the estrangement of Connie. That is the tragedy, by trying to protect his family, Micheal ends up destroying it.