He fell to last after his pit stop but managed to pass the two Williams of Sergey Sirotkin and Lance Stroll in the closing laps.
"Great work guys. So happy for England as well [in the Football World Cup] - it's a beautiful Sunday. Happy Sunday everyone," a delighted Hamilton said on team radio after the race.
"I feel very grateful; Grateful for a solid weekend. My guys continuously push the boundaries and never give up. This is a great day. I enjoyed the race, for me it's the best French GP I've ever had. I haven't thought about [the championship lead], but that's where I want to be."
A chaotic opening lap saw a couple of different incidents completely change the landscape of the race.
Ferrari's Sebastian Vettel made a good start but took out the Mercedes of Valtteri Bottas at the first corner and saw both drivers limp back to the pits with damage.
The Toro Rosso of Pierre Gasly crashed into the Force India of Esteban Ocon that did significant damage to both cars and forced them out.
Because the field was bunched up other drivers lost spots trying to avoid getting caught up in the incidents.
Hartley leapt to 13th by the end of the first lap thanks largely to the drama ahead of him.
Vettel and Bottas began climbing through the field however having had the benefit of pitting under a safety car and it didn't take long for them to be back among the points. Vettel got a five second time penalty for causing a collision.
Vettel made his way to fifth to limit the damage but he conceded his championship lead to Hamilton.