Francois, who is entering his 10th season, will provide depth after Lions defensive end Ezekiel Ansah was placed on the physically unable to perform list on Tuesday.
The 6-foot-3, 313-pound Francois appeared in 12 games with the Green Bay Packers and New England Patriots last season. He also played in all three postseason games, including the Super Bowl, with the Patriots.
A seventh-round draft pick of the San Francisco 49ers in 2009, Francois has 164 total tackles (97 solo), 12.0 sacks, one forced fumble and one fumble recovery in 121 games.
Sankey appeared in six games with the Indianapolis Colts in 2017 before he was cut in November. He was signed by the Baltimore Ravens two weeks later and spent the remainder of the season on their practice squad.
In other moves Thursday, Detroit waived linebacker Al-Rasheed Benton and offensive lineman Beau Nunn while placing linebacker Devon Kennard and defensive end Cornelius Washington on the active-non football injury list.