Richard Gasquet and Jo-Wilfried Tsonga clinched the vital rubber with a 5-7, 7-6 (7/4), 6-2, 7-5 success over Chris Guccione and Lleyton Hewitt at Mouilleron-le-Captif in western France.
France's reward was a last eight clash with Germany, who took an unbeatable 3-0 lead over five-time former champions Spain in Frankfurt earlier .
That quarter-final is scheduled for .
France skipper Arnaud Clement took a gamble , linking up Gasquet and Tsonga for the first time in a Davis Cup doubles rather than deploying the more experienced doubles player at his disposal, Julien Benneteau.
It worked a treat with the French duo getting the better of an Australia pair that arrived on the indoor clay court unbeaten in five Davis Cup outings.
Trailing after the first set they fought back to take a tense second set tie break before storming through the third set and holding their nerve to get the necessary break to claim the fourth set.
That win put France into their fifth quarter-finals of the 114-year-old competition.
The French went into the middle day of the tie with the upper hand after Tsonga and Gasquet saw off Hewitt and Aussie teenager Nick Kyrgios respectively .
France beat Australia in their last meeting in 2001 when the French won the title in Melbourne.
Australia have won the trophy 28 times and last in 2003.