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Fly-half Bernard Foley added the rest of the points with four conversions and two penalties, making it seven Tests in a row for Australia for the first time since 1999-2000.
The Wallabies had the match wrapped up by half time, going into the break with a 20-6 lead. Foley's third-minute penalty got the hosts moving and they were 10-0 in front after eight minutes thanks to Skelton.
Brice Dulin got the French out of the blocks with a penalty but Foley responded with another three-pointer before the home side took advantage of the yellow card shown to Rabah Slimani and increased their lead yet again.
With the French prop in the sin bin for tackling without the ball, Australia claimed a second try, Folau stretching over in the corner on 28 minutes.
Foley went on to add a second conversion to make it 20-3 and, despite Maxime Machenaud fighting back with a penalty just before half time, the Wallabies looked set for an easy second half.
The home side continued to run the game after the restart, increasing their lead inside two minutes as Folau crossed for the second time, with flanker Hooper adding a fourth Australia try after an hour.
France responded with only a couple of penalties and a single converted try from Guilhem Guirado in the second half and it finished 39-13, condemning them to their 13th loss in 19 Tests and upping the pressure on coach Philippe Saint-Andre.