Antoine Devaux scored the winner in the 1-0 third-round victory in the 34th minute as the hosts beat a much-changed Monaco side.
Sochaux claimed a 3-2 win over Montpellier after extra-time.
Extra-time goals from Sebastien Corchia (115) and Roy Contout (118) put the hosts 3-1 ahead, meaning Benjamin Stambouli's 120th-minute goal counted for nothing.
The match had been tied at 1-1 after 90 minutes, with Sanjin Prcic putting Sochaux ahead after 39 minutes and Jonas Martin levelling from the spot in the 48th minute.
Martin was sent off in the 103rd minute, handing the initiative to Sochaux.
Evian came from behind to win 2-1 at Guingamp.
Mustapha Yatabare put Guingamp ahead in the 25th minute, but Moudou Sougou equalised in the 56th minute and Cedric Cambon got the winner 12 minutes later.