World record holder and defending champion Kristof Milak of Hungary led until the final stretch when Marchand, who already has gold from the 400m medley, made his dramatic surge, roared on by the home crowd.
Marchand, who will also go for gold later on Wednesday in the 200m breaststroke, finished with a new Olympic record time of 1min 51.21sec.
Milak, who made a superb start and looked to be dominating the race, was unable to hold off the Frenchman and finished 0.54 seconds behind to collect silver while Canada's Ilya Kharun claimed the bronze.
Marchand, whose parents were both Olympic swimmers, received a rapturous reception from a crowd waving French flags and his hero status will only be enhanced by this latest performance.
The 22-year-old's win in the 400m individual medley on Sunday had given the country their first swimming gold since 2012.
Marchand is trained by Michael Phelps' former coach Bob Bowman.