Les Bleus, who entered the final match of the group stage with six points from their first two matches, were a virtual certainty to reach the knockout round thanks to their emphatic wins against Honduras and Switzerland.
Needing only a draw to lock up first place, France neutralized the attacking threat of Ecuador, which had been reduced to 10 men following Antonio Valencia's straight red card in the 50th minute.
La Tri, unable to conjure a goal, finishes third in Group E to become the lone South American nation to miss out on the knockout round.
The first half of Wednesday's affair offered little in the way of scoring opportunities, but the best chance fell to Ecuador in the 41st minute when Enner Valencia connected on Michael Arroyo's cross with a powerful header, but Hugo Lloris managed to deny the Pachuca striker.
France emerged from the intermission and nearly grabbed the lead within two minutes of the restart when Bacary Sagna's low cross was turned on frame by Antoine Griezmann, but Alexander Dominguez pushed the attempt onto the post to allow Ecuador to clear the danger.
Ecuador's task of claiming a win was made more difficult in the 50th minute when Antonio Valencia was sent off for an vicious sliding challenge on Lucas Digne.
But La Tri managed to produce a gilt-edged scoring opportunity just four minutes later when Christian Noboa got through on goal only to send his attempt horribly wide of the post.
Paul Pogba spurned a tremendous chance to preserve France's unblemished record in the group stage when he got on the end of Moussa Sissoko's cross from a short corner kick in the 73rd minute, but the Juventus midfielder sent his header just inches wide of the post.
France produced a few more half-chances in the closing stages of the match, but with Switzerland cruising to a 3-0 defeat of Honduras in Group E's other fixture, both sides eased off the pedal to finish scoreless at the historic Maracana.
Les Bleus will return to action in the round of 16 on Monday against Nigeria, which finished as runner-up in Group F.