Through luck, determination, bad finishing and brilliant goalkeeping by Alexander Dominguez, Ecuador resisted even after captain and Manchester United winger Antonio Valencia was ordered off early in the second half for a studs up challenge on Lucas Digne.
The result was disappointing for French coach Didier Deschamps but was enough to take top place with seven points and the easier of the possible second round ties next Monday. Switzerland's 3-0 win over Honduras in the group's other game gave them second place and a tough match against Argentina on Tuesday. Ecuador become the first South American side to be knocked out of this World Cup.
Karim Benzema, scorer of three goals in wins over Honduras and Switzerland, kept his place in the side, but France missed the creativity of Mathieu Valbuena and Yohan Cabaye, the latter absent due to suspension and replaced by Southampton's Morgan Schneiderlin.
Les Bleus controlled much of the first half, but only sporadically troubled Alexander Dominguez in the Ecuador goal.
The Ecuadorean 'keeper held a crisply-struck volley from Moussa Sissoko with 15 minutes played and did well to palm the ball over the bar when Paul Pogba got his head to an Antoine Griezmann free-kick.