Australia punished late French errors to snatch a 23-21 victory at the death with Noah Lolesio kicking the match-winning penalty in Brisbane.
Les Bleus led by 15 points in the first half after two Gabin Villiere tries but Wallabies captain Michael Hooper's late try closed France's lead to one.
France then kicked a penalty to touch but fumbled the resulting line-out and Australia won the decisive penalty.
The sides meet again on Tuesday in the second game of the three-match series.
It was Australia's second Test victory since the 2019 World Cup against a French side that have rested most of their Test starters.
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