It was intended to be a franchise, but not continuing the story of Kratos. There's a teaser for a game set in modern times, with soldiers exploring the temple on Cronos' back, at the end of the first game. Presumably, Kratos still would have shown up, but in the same capacity that Poseidon or Zeus shows up in the original; maybe as often as Athena, or even as much as Ares, but not as the protagonist.