Paris St Germain needed a second-half goal from Stephane Sessegnon to beat fourth division Montlucon 1-0 on Sunday and advance to the last 32 of the French Cup.
Benin midfielder Sessegnon tapped in from a corner on 52 minutes to make sure last season's losing finalists survived the first round involving top-flight clubs.
Monaco had earlier struggled to overcome fifth division Blagnac, needing an own goal from defender Frederic Marquet on 21 minutes to win 1-0.
Olympique Lyon, who beat PSG in last season's final, saw their round of 64 tie at amateurs Concarneau postponed for the second day running on Sunday because of a frozen pitch. No new date was set.
In the evening's later tie, Besancon held Marseille to a 1-1 draw.