From a reduced peloton, Groupama-FDJ rider Molard attacked 1.2km from the line and with his rivals playing mind games behind, crossed the line first to claim his second professional victory.
"It's fantastic to bring a second victory to Groupama-FDJ," Molard said. "I live in Antibes and I knew the course like the palm of my hand.
"Since the profile of this Paris-Nice was announced, I was delighted with such a finale which suited my qualities.
"I knew that in the Cote de la Colle-du-Loup it was useless giving my all, you just had to follow. I knew that the decision would come in the finale. I was expecting attacks and I knew I would have lost in a sprint.
"I really needed to attack before the sprint. I tried several times and it worked. It's just great. This Paris-Nice is nice for the French and for my team. It's a great reward for all the sacrifices we make in training in the winter."
Team Sky suffered a bad day as its team leader Wout Poels, who was second overall, crashed out seven kilometres from the finish in the 198km stage from Sisteron to Vence, suffering a broken collarbone.
“I just couldn’t hold on in that corner anymore. I’d gone full into it,” Poels said, “It’s so disappointing because I had been feeling really, really good. But that’s life sometimes.
“I’ll make a plan now with the doctors about what to do with my collarbone. I had planned to have a period of rest after Paris-Nice anyway, so we will see.”
Overall leader Luis Leon Sachez had a quiet day in the saddle as his Astana team controlled the race and leads Julian Alaphilippe (Quick-Step Floors) by 22 seconds and Marc Soler (Movistar) by 26.
"I'm sorry for Wout Poels who crashed, he was doing very well," Sanchez said. "But all my rivals are hard to beat even I still have a little bit of a gap.
"Esteban Chaves, for instance, has a great team [Mitchelton-Scott] and is very motivated. But I also have a great team with me and great team-mates like Jakob Fuglsang. We're going to keep fighting and see how it goes."
Stage 7 takes the peloton over 175km from Nice to Valdeblore La Colmiane and ends with a 16.3km ascent at an average gradient of 6.2 percent.