France took control of the game in the third quarter, with a Celine Dumerc three-pointer sparking a 10-0 run that put them on top 43-34.
Their lead was 52-39 on Emilie Gomis's free throws, but the Opals began to rally.
Australia finally regained the lead with four minutes left to go through Samantha Richards but they could not hold it.
France appeared to have it won when Belinda Snell missed a three and Gomis broke clear, but she missed a wide-open lay-up, and Snell made her pay with a half-court shot.
However, France held their nerve to edge overtime.
Gomis led France with 22 points, while Dumerc contributed 13. Suzy Batkovic scored 17 for Australia.
Meanwhile, Great Britain women's coach Tom Maher believes his team's lack of experience cost them a first-ever Olympic win as they let slip a late lead against Canada.
Britain had been up 61-57 with six minutes left in the game but then seemed to fall apart, allowing Canada to romp home on a 16-4 charge to win 73-65.
Britain were the architects of their own downfall, turning the ball over several times with careless passes.
'I think it was composure,' said Maher, who is coaching at his fifth Olympic Games. 'We threw the ball away.'
Elsewhere, China continued their impressive start in Group A as they cruised to a 83-58 victory over Croatia, while Turkey beat the Czech Republic, Russia beat Brazil and the USA ran up a 90-38 victory over Angola.