Caen, who had started their campaign with a shock 2-1 win at Olympique Marseille, picked up three points again, this time against last season's runners-up. Midfielder Ismaila N'Diaye scored the winner with a fine volley on 77 minutes.
Visitors Lyon twice fought back from a goal down with two goals from forward Bafetimbi Gomis but were reduced to 10 men with a second booking for Anthony Reveillere just before half-time.
Lyon, who had been held to a 0-0 draw by Monaco last week, face several weeks without their captain, Brazilian defender Cris, who was substituted around the hour mark because of a pulled thigh muscle.
"We have lots of injury worries but that's no excuse," Lyon coach Claude Puel, who was already missing Argentine striker Lisandro Lopez, told reporters. "We must raise the level of our game and we must do it fast."
A late goal from Etienne Didot gave Toulouse a 2-1 win at Girondins Bordeaux, putting them at the top of the table and level on points with Caen.
Bordeaux, champions in 2009, had started with a 1-0 defeat at Montpellier and are still without a point after two games.
"Losing your first match can happen, especially when it's an away game, but losing the first two is a nuisance," Bordeaux president Jean-Louis Triaud told reporters. "What I didn't like was that we were not aggressive enough."
Paris Saint-Germain, who have struggled in recent years, extended a relatively promising start with a 0-0 draw at Lille, regarded as one of the strongest sides in the league.
The capital club are in fourth after two games, two points off the pace.
