Monaco into French Cup last 16 as Nantes go out
Ben Yedder struck his first from the penalty spot and then netted twice more in the second half after Stone Mambo had equalised for Ligue 2 side Rodez.
Malik Tchokounte's header earned second-division Laval a 1-0 win at Nantes, who won the competition in 2022 but were thrashed in the final by Toulouse last year.
Nice held off Bordeaux to advance 3-2 with Morgan Sanson notching a brace for the team second in the top flight.
Brest, flying high in third place in Ligue 1, avoided an upset away to fourth-tier Trelissac, coming from behind to win 2-1 with late goals from Kenny Lala and Martin Satriano.
Paris Saint-Germain play third-division Orleans in Saturday's late tie for a place in the last 16.