The Wallabies, who rallied from 8-0 down to lead 13-11 at half-time, held off a late French charge with Camille Lopez missing a drop goal in the last action of the match.
Michael Cheika's side, who kicked off their tour with back-to-back wins against Wales and Scotland, next play Ireland and England, as they eye a Grand Slam of Home Nations for the first time since 1984.
Both sides scored three tries apiece -- the Wallabies first a penalty try followed by one from Bernard Foley, a late call-up for the injured Quade Cooper, and a spectacular effort from Tevita Kuridrani.
It was a return to reality for France who had been aiming to build on their morale-boosting 52-8 thrashing of Samoa.
Winger Virimi Vakatawa, fly half Jean-Marc Doussain and centre Wesley Fofana scored France's tries.
France next play New Zealand in Paris on November 26 for the first time since they were humiliated 62-13 at the World Cup in 2015.