PSG, playing at Annecy without their talismanic injured Sweden striker Zlatan Ibrahimovic, had midfielder Cabaye sent off in the 62nd minute for a second bookable offence.
PSG, who have taken five points from their first three games, dominated possession but struggled to create chances, with their Uruguay striker Edinson Cavani missing his best chance in the 26th minute when he slipped inside the area.
Another attempt by Cavani, set up by Lucas, in the 70th minute, was knocked away by Evian goalkeeper Jesper Hansen.
PSG, chasing a third successive title, are third in the 20-team table, one point behind Bordeaux, who visit Nice on Saturday, and St Etienne, who host Stade Rennes on Sunday.
Evian, who created chances in added time as they chased a winner, moved off the bottom of the table to 18th with their first point of the season. The hosts, routed 6-2 by Rennes last Saturday, had conceded nine goals in their first two games.
It was the second competitive match for PSG's Brazil centre back David Luiz since he joined the club from Chelsea in June for an estimated 50 million pounds ($83.5 million), making him the world's most expensive defender.
Besides losing Ibrahimovic, who is out for several weeks with a rib injury, Italy midfielder Thiago Motta was also missing after being headbutted by Bastia's Brandao after last week's match.
On Thursday, the French football league suspended Brandao for four weeks, pending a hearing on Sept. 18.
Meanwhile, the Paris prosecutor's office told Reuters Brandao would be judged before a criminal court for "premeditated voluntary violence" in a sports context.
It was not immediately clear what potential sentence he could face.
- Sports & Recreation
- Zlatan Ibrahimovic
- Edinson Cavani