In front of a crowd of over 50,000, Sam Kerr came off the bench in the second half and the talismanic striker duly converted his penalty in the shootout.
Australia goalkeeper Mackenzie Arnold missed a game-winning chance in the shootout when his kick hit the post, but VAR saw both feet off his line for the first time, after which he made two saves from Kenza Daly.
Vicky Becho missed France’s 10th penalty and it was left to Vine to beat France’s substitute goalkeeper Solenn Durand, who had been specially sent on for the shootout.
“You girls should be proud tonight. He played an extraordinary match,” said French coach Hervé Renard.
Sweden will face Spain in the second semi-final on Tuesday.
Spain beat the Netherlands 2-1 in extra time and Sweden beat 2011 champions Japan by the same score on Friday, meaning there will be a new name on the World Cup trophy this year.
Outgoing holders the United States and former champions Norway and Germany are already out.