Ajaccio, who have not impressed since getting relegated from Ligue 1 last season, travelled to Borgo for their eighth-round tie on Saturday and were taken all the way to extra-time by their hosts, before claiming a 3-2 win.
Angers were not afforded the luxury of an extra 30 minutes, however, as they were beaten 2-1 by fifth-tier relegation-strugglers Dinan-Lehon, despite the away side taking a 15th-minute lead.
Like Angers, National Ligue team Istres were also dumped out of the competition by fifth-tier opposition, with Bressuire claiming a 2-1 victory thanks to Quentin Brebion's extra-time winner.
Clermont and Le Havre also had their cup runs cut short by lower-league sides, with Epinal beating the former on penalties after a 1-1 draw, while Erick Mombaerts' men lost 2-0 at home to Boulogne.
Brest and Tours both needed penalties to avoid upsets, beating Paris and Stade Bordelais after drawing 0-0 and 2-2 respectively.
Proving that not all the bigger sides were off-colour on Saturday, Auxerre beat Sarreguemines 4-0 on the road, while Nancy claimed a fine 3-1 triumph at fellow Ligue 2 high-flyers Troyes.
Niort, Chateauroux, Arles, Nimes, Laval and Orleans are the other Ligue 2 sides progressing to the next round, with the latter beating US Laon in emphatic fashion, winning 7-0.
Flying the National Ligue flag in the next round will be Le Poire-sur-Vie, Dunkerque and Lucon, while Club Franciscain and St. Maur Lusi also squeezed through.
There were also wins from Plabennec, Saint-Priest, Beauvais and Concarneau from CFA, while CFA 2 sides Andrezieux, Jura Sud, Cholet and Saint-Louis Neuweg will likely have the odds stacked against them in the next round after securing their respective places.
