"It was my most emotional win, by far. If there was a race I wanted to win this year it was clearly Paris," said Vergne.
"To have done it in such a way today with pole position and a race win was absolutely amazing."
Brazil's reigning champion Lucas di Grassi finished second for Audi Team Abt with Britain's Sam Bird third for DS Virgin Racing.
There was last-lap mayhem with Bird, who remains second overall on 116 points to Vergne's 147, finishing on three wheels.
The Briton, following Di Grassi, had smashed into Andre Lotterer's stricken Techeetah at the last corner with the German's car running out of power and coasting home after being in second place.
"We actually discussed in the driver’s briefing this exact thing where you cannot move under braking. You cannot do a late swerve when people are obviously going to be overtaking you," fumed Bird, blaming Lotterer for a change in direction.
"It’s not correct in any form of motorsport... it’s too much from Andre."
(Writing by Alan Baldwin in Baku, editing by Pritha Sarkar)
