The Field Records for Fran state that the princess awoke 30 years after the fall of Dalmasca to Garlemald. They don't give an exact time on when she awoke, but those same field records mention that the events of the Ivalice raids take place during the same year, as it mentions that Fran hadn't seen Ba'Gamnan's crew for 30 years. So the princess has, at least for all intents and purposes, been awake for less than a year (as far as game time is concerned).