Nice became the first top-flight side to fall to a club from a lower league in this season's French Cup when they lost 2-1 at third division strugglers Plabennec in the round of 64 on Sunday.
Olympique Marseille, who have lifted the Cup a record 10 times, later struggled to move past fifth division Trelissac 2-0 with a goal in each half from winger Hatem Ben Arfa and midfielder Benoit Cheyrou.
A streaker braved freezing temperatures to invade the pitch in the second half in one of the few highlights of a dull game.
"We have qualified and that's all that matters," Marseille coach Didier Deschamps told Eurosport television. "Against teams from lower divisions, you never know what can happen."
Nice opened the scoring early on against Plabennec through forward Loic Remy but the home side, second from bottom in the third division, responded with two goals from striker and captain Jean-Michel Abiven.
Paris St Germain qualified in comfortable fashion, thrashing amateurs Aubervilliers 5-0 with two goals from Peguy Luyindula in late action at Parc des Princes.
The Ligue 1 sides entered the event this weekend. Twelve matches have been postponed because of wintry conditions.
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