Francois, who started 11 games this past season and has 25 starts in his FSU career, had considered entering the NFL draft or transferring to another college program.
"While my dream is to play in the NFL, at this time I feel that there are areas both within my game and my life that I need to improve upon to succeed at the next level," Francois wrote on Instagram. "I don't take for granted the privilege it is to wear the Garnet & Gold. I love Florida State, my brothers and know I have much more to offer."
Francois and redshirt sophomore James Blackman are expected to compete for the starting job in the 2019 season under new offensive coordinator Kendal Briles. Blackman started most of the 2017 season after Francois suffered a knee injury in an opening loss to Alabama.
Francois passed for 3,350 yards and 20 touchdowns as a freshman in 2016, but he struggled at times this past season, completing 57.3 percent of his attempts for 2,731 yards with 15 touchdowns and 12 interceptions.
"I intend to become the leader my teammates need me to be because we have some unfinished business to take care of," Francois wrote on Instagram.