Debinha equalised in the 58th, finishing off a quick passing movement into the area, controlling the ball with the outside of her leg then firing in a right-footed shot.
Le Sommer was replaced in the 66th by Vicki Becho to add some extra speed to the French attack.
Leticia pushed a hard strike over the crossbar to keep Brazil level and Selma Bacha hit the side netting with her shot from the right in the 75th, unable to break the deadlock for France.
Renard, who was a doubtful start after picking an injury in the opening game, stepped up when the French most needed it.
The veteran defender was unmarked in perfect position in the 83rd to meet a corner with a header that she nudged powerfully into the top right of the net.
France have four points, one more than Brazil ahead of the last group games on Wednesday. The French will play Panama in Sydney, and Brazil will take on Jamaica in Melbourne.
- AP