Montpellier, who have never won the French title, are on 79 points with PSG on 76 after they thrashed Stade Rennes 3-0 home thanks to a hat-trick by Nene.
"We believed in it until the end. What the lads did was fabulous," Montpellier coach Rene Girard told French TV Canal+.
Montpellier travel to basement side Auxerre, who are relegated, next weekend and PSG play at Lorient.
"Nothing has been achieved. We have a game left at Auxerre and it would be a disgrace to lose there," Ait Fana told reporters.
Both clubs secured Champions League places and Lille, who surrendered their title at the Mosson stadium and are on 71 points, will feature in the qualifying round.
"It's beautiful," a tearful keeper Geoffrey Jourdren said.
Girondins Bordeaux climbed into the Europa League qualifying spot as Yoan Gouffran scored from the penalty spot in stoppage-time to help his side beat Lorient 1-0.
Auxerre, who have been in the top flight since 1980, were relegated to Ligue 2 after they lost 3-0 at Marseille.
France and Marseille striker Loic Remy left the pitch because of an adductor muscle injury which could rule him out of the European Championships.
NENE SHINES
In Montpellier, the hosts were about to settle for a draw when Ligue 1 top scorer Olivier Giroud ran through from the middle of the pitch to set up Ait-Fana who poked the ball into an empty net.
The unheralded leaders, who were supported by an unusually packed crowd, had their chances to take the lead earlier, but midfielder Jamel Saihi failed to score in the 23rd minute after Giroud had superbly set him up.
In a tense first half, both teams were too cautious to threaten the opposition goalkeepers, while Eden Hazard, who was carrying Lille's faint hopes of retaining their title, produced a poor performance.
The Belgian woke up after the interval but he was denied the opener when Jourdren tipped away his curling free-kick.
His counterpart Mickael Landreau also pulled off a pair of beautiful saves before substitute Ait-Fana gave his side their 16th home victory of the season.
At the Parc des Princes, PSG also struggled before the break, but Nene and Jeremy Menez inspired them to an easy win early in the second half.
"It will obviously will be more difficult to win the title," coach Carlo Ancelotti said.
"But tonight we achieved an important goal, which was to be in next season's Champions League. I'm very happy to have chosen PSG and I hope we will be better in the future.
Nene scored the opener from close range in the 47th minute after Jeremy Menez ran through the right side to set him up.
The Brazilian curled a superb free-kick into the top corner on 58 minutes and netted his 21st league goal from the penalty spot.
