Marquez had started on pole position for the fifth time in five races this season but had to fight back from 10th place at the end of the first lap after a poor getaway at the sunny Le Mans circuit.
He reeled in Italian Valentino Rossi, who had led from the start, with 16 of 28 laps to go and pulled away convincingly to become the first rider to win five races in a row from pole since Australian Mick Doohan in 1997.
Rossi finished second on a Yamaha, for his 150th podium in the top category, with Spaniard Alvaro Bautista third on a non-works Gresini Honda for his first top three finish since 2012.
"Today was a little bit harder than the other races, especially in the beginning," grinned Marquez, the first rider since Italian great Giacomo Agostini in 1972 to win the first five races of a season in the top class.
"On the first two corners I was too calm, I need to be more aggressive like last year because many riders overtook me," added the Spaniard, who ran wide as compatriot and double champion Jorge Lorenzo went past.
"But I'm really happy for this victory. We must enjoy the moment because five victories in a row is not easy," he told Britain's BT Sport. Marquez now has a maximum 125 points with Honda team mate Dani Pedrosa, who finished fifth, on 83 and Rossi on 81.
As Rossi opened a small gap at the front in the early stages, Marquez recovered his balance and moved swiftly back through the field before passing Rossi when the Italian made a mistake under braking into a corner.
"It's a pity because I made a mistake in the crucial part of the race," said Rossi. "I was pushing very much, Marc was a bit faster than me but not a lot so I could fight with him... it was too easy for him.
"Maybe he can beat me anyway but with a big fight it would have been more fun.
"We will try in Mugello," said the Italian, referring to the next race in Italy on June 1.
(Writing by Alan Baldwin in London, editing by Pritha Sarkar)
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