Canada also began their quest in confident fashion as singles wins for Denis Shapovalov and Felix Auger-Aliassime assured them of victory in their opening Group D tie against Argentina in Manchester.
Germany posted a 3-0 victory over Slovakia in Zhuhai, China which is hosting the Group C matches.
Australia, the 28-time Davis Cup champions who lost to Italy in the final last year, were given a flying start when Thanasi Kokkinakis battled to a 7-6(4) 7-6(3) win over the higher-ranked Arthur Fils, recovering a 2-4 deficit in the second set.
France responded with their number one Ugo Humbert dispatching Alexei Popyrin 6-3 6-2.
But Australia got the win as Ebden and Purcell teamed up to beat experienced French duo Pierre-Hugues Herbert and Edouard Roger-Vasselin 7-5 5-7 6-3.
It was the third year in a row that Lleyton Hewitt's Australia beat France at the Davis Cup Finals group stage.
Canada, the 2022 Davis Cup champions, beat Argentina 2-1 after left-hander Shapovalov defied his slip down the rankings to beat 31st-ranked Francisco Cerundolo 7-5 6-3.
"I feel great," Shapovalov said. "The last time I played in the Davis Cup we won it so it was nice to be back and playing at such a high level."
Auger-Aliassime was then equally assured in a 6-3 6-3 victory over Sebastian Baez to put Canada 2-0 ahead.
Argentina managed to get on the board in the doubles.
Germany proved far too good for Slovakia as Maximilian Marterer beat Lukas Klein 6-4 7-5 before Yannick Hanfmann beat Jozef Kovalik 3-6 6-3 7-6(3). Tim Puetz and Kevin Krawietz then completed the job with a doubles victory.
Sixteen nations are competing in four groups in Manchester, Bologna, Valencia and Zhuhai with the top two from each group moving through to the Davis Cup Final 8 Knockout Stage which is being held in Malaga, Spain in November.
In the day's other tie Belgium beat the Netherlands 2-1 in Group A being hosted in Bologna.
Reigning champions Italy begin their quest in Group A on Wednesday against Brazil although they will be without newly-crowned US Open champion Jannik Sinner.
