A first-half goal by defender Jacques Faty and one near the end from forward Sloan Privat gave Sochaux victory but Lyon, who visit Liverpool in the Champions League on Tuesday, stayed a point ahead of Girondins Bordeaux, who lost 1-0 at Auxerre.
"This is frustrating but now we have to think about Liverpool," Lyon's Brazilian midfielder Ederson told reporters. "Of course, we would have preferred a win before going there but we need to bounce back straight away."
Bordeaux, who ended Lyon's seven-year supremacy by taking the title last May, missed a penalty through Argentine striker Fernando Cavenaghi in the first half and saw Slovenia forward Valter Birsa convert a second-half penalty for Auxerre.
"Things have not gone our way lately but what we have to do is get straight back to work," Bordeaux defender Mathieu Chalme told reporters. "The best way to get our confidence back would be to win in Europe."
"People were starting to have a go at us but we just held tight and showed tonight that we are a real team," Marseille midfielder Benoit Cheyrou told reporters.
