The 28-year-old Vergne dominated the 49-lap race on the streets of the 7th arrondissement from pole position for his third victory of the season from eight races.
"I can't find words," said the Techeetah driver after taking the checkered flag. "It's an incredible feeling, by far my best victory."
It looked set to be a another one-two for Techeetah with Vergne's teammate Andre Lotterer running in second place until slowing dramatically on the final lap because of depleted charge in his car.
Defending champion Lucas di Grassi of Brazil came past the German with very little room to spare before Britain's Sam Bird (DS Virgin Racing) appeared to misjudge the pace of Lotterer's car, ploughing into it, with debris flying everywhere.
Incredibly, Bird crossed the line on just three wheels, but with his car wrecked, to take the final podium place. Lotterer slipped to sixth with Venturi's Maro Engels going past for his best finish in Formula E, followed by former champion Sebastien Buemi in fifth.
It helped limit his losses in the title race to Vergne, but he trails the Frenchman by 31 points with just four rounds remaining.
Bird was furious with Lotterer, claiming he had tried to prevent him passing. "I don't think you can change direction like that," he said.
He and Lotterer had also tangled after he overtook Bird for second place following the pit-stops, while di Grassi had a similar experience as he tried to pass the Techeetah driver later in the race.
"The way Andre behaved on track was not very professional," claimed di Grassi, who was finishing on the podium for the third straight race after a sorry start to his championship defence in the Audi Sport entry.
Vergne, looking for Formula E victory in Paris at the third time of asking, had to hold off a determined Bird, who had won the previous round in Rome,
in the opening laps with Lotterer keeping close company as well in third.
The trio had pulled well clear of the chasing pack by the time of the pit stop to switch cars and it was Vergne who extended his advantage with a quicker change than his title rival.
Bird was overtaken by both Lotterer and di Grassi and looked to be losing more ground on Vergne in the title race until the incidents on the final lap.
The championship looks set to be a two-way battle heading into the next round in Berlin in three weeks time with third-placed Felix Rosenqvist a further 30 points adrift of Bird after taking just four points in Paris for Mahindra Racing.