Didier Deschamps' men had racked up eight goals in their first two games in Brazil, beating Honduras 3-0 in Porto Alegre before hammering Switzerland 5-2 in Salvador.
However, despite the dismissal of Ecuador captain Antonio Valencia just after the break in Rio, Les Bleus were unable to find a way past an inspired Alexander Dominguez, though the point was still sufficient to see France finish one point clear of the second-placed Swiss.
"But we have not lost and we are qualified for the next round. We are proud of our qualification for the last 16.
"We came across a good goalkeeper [Dominguez], who had to make several saves.
"I hope that in the next game those shots go in, but this game proves that there no easy opponents in the World Cup."
Ecuador had needed to win at the Maracana in order to progress. As it is, they are heading home after finishing third on four points, two shy of Switzerland.