A packed Ernst-Happel-Stadion cheered when Austria took the lead in the first half - after a dream attack.
Schlager drove up with the ball before finding Arnautovic, who in turn released the ball on a running Laimer.
A perfect entry later and Andreas Weimann could easily put in his first national team goal for Austria.
Before that, France had had a great opportunity to take the lead, but goalkeeper Patrick Pentz stopped Karim Benzema with a sharp double save.
Mbappé saved points
France got off to a good start in the second half.
Kingsley Coman was given a chance to change things around.
The guests in blue then replaced Kylian Mbappé and it certainly had an effect.
In the 83rd minute, he broke the home defense before finishing right up in the net to 1-1.
The same Mbappé then had a shot in the crossbar but no more goals were scored in the match.
France has now scored two points in three matches in the Nations League.
In the second match of the group, Croatia defeated Denmark 1-0.