The competition's reigning champions have just two points from three Group A1 matches, having lost at home to Denmark and drawn away to Croatia in their opening two games.
It could have been even worse for Les Blues at Ernst Happel Stadion as they trailed to a 37th-minute Andreas Weimann strike until substitute Kylian Mbappe leveled up late on.
With three games to go, Didier Deschamps' side are four points behind leaders Denmark and two behind Austria and Croatia, with only one team advancing to next year's finals.
Patrick Pentz produced a fine save to keep out Karim Benzema in the opening 17 minutes, but France were otherwise frustrated by Austria in the first half.
The hosts probed away and found a breakthrough when Konrad Laimer was played in by Marko Arnautovic and in turn, picked out Weimann for a simple finish from six yards.
Arnautovic nearly doubled Austria's lead before the interval after swiveling past William Saliba and getting a shot away, which Hugo Lloris comfortably kept out in the end.
Benjamin Pavard had a long-range effort saved by Pentz and Kingsley Coman blazed over from close range as the inevitable France onslaught arrived early in the second half.
France appeared to run out of steam until Mbappe, brought on in the second half after recovering from injury, linked up with Christopher Nkunku and rifled into the roof of the net.
Mbappe would have snatched a late winner in the final few minutes if not for a fine Pentz save to push his strike onto the frame of the goal from a one-on-one.
What does it mean? France remain winless
Eight months on from beating Spain to win the previous Nations League tournament, France face a battle to stay in the top tier of groups, never mind advancing to the finals.
Les Blues will now likely have to win their remaining matches and hope other results go their way if they are to leapfrog the other three sides in their group and finish top.
As for Austria, they have now won two of their three games under Ralf Rangnick, who has hit the ground running since his disappointing spell as interim Manchester United boss.