Les Bleus travelled to Suncorp Stadium knowing history was against them, France's last away win over Australia having come 11,330 days ago on June 30, 1990.
But a pair of tries from Gabin Villiere put France in command, with Australia unable to respond until Brandon Paenga-Amosa went over in the 34th minute to make it a 15-7 half-time deficit.
Noah Lolesio reduced the gap to five points from the tee and his second penalty sandwiched three-pointers from Louis Carbonel and Melvyn Jaminet to keep the Wallabies in touch.
Australia captain Michael Hooper backed over the line nine minutes from time and Lolesio knocked over a simple conversion to fray France nerves as they were left to nurse a one-point advantage.
Lolesio had the chance to be the hero in the 77th minute but his drop goal drifted wide of the right-hand upright.
It looked as if Australia's chance had gone but France inexplicably failed to get the ball out of play from a lineout with the clock in the red, conceding possession and allowing Australia to earn a decisive penalty that Lolesio converted from in front of the posts.