Dan Mullen, who is in his first season as head coach, stuck with the experience of the third-year sophomore Franks, who went 3-5 as a starter last season.
Redshirt sophomore Kyle Trask will serve as Franks' backup.
Franks, a Florida native, showed a strong arm but struggled with consistency as a redshirt freshman last season. He completed 54.6 percent of his passes with 9 touchdowns and 8 interceptions in 11 appearances.
Jefferson caught 91 passes for 999 yards and 4 touchdowns in two seasons with the Rebs.
Florida opens at home against the Buccaneers on Saturday night. A week later, the Gators begin conference play at home against Kentucky.