Championship leader, and fellow four-time world champion, Sebastian Vettel of Ferrari was third, three-tenths off the pace, ahead of Max Verstappen and his Red Bull team-mate Australian Daniel Ricciardo.
The Briton made it two easy wins for his country in one day, after England's progression to the second round of the World Cup with their cruise to a 6-1 victory over Panama.
Hamilton extended his record run of points-scoring finishes to 33 successive races.
The four-time world champion, making the most of his upgraded Mercedes engine, led from start to finish, bar one lap following a pit stop, as he claimed his first win in France, his third this year and the 65th of his career.
Mercedes claims the engine, known as Phase 2.1, is better still than the Phase 2 upgrade it had planned to use in Canada. "The team in Brixworth have moved mountains to deliver the updated unit in time for France and we are looking forward to racing it in anger both here and in the races that follow thick and fast in the weeks ahead".
"After the first attempt I saw that we are maybe so I knew that with a really unbelievable lap I maybe have a chance but it didn't come", he added, saying that P3 isn't bad.
However, Valtteri Bottas missed out on most of the second practice session after suffering a water leak on his auto after just seven laps.
He was unhurt and after climbing from his auto walked back to the pits with his helmet firmly in place, before the session resumed and Hamilton scorched to pole on his final flying lap.
Vettel took the soft tyres and emerged in 17th, his race already reduced to damage limitation.
But there his progress stopped and he was able to make a late pit stop for fresh tyres, serving his penalty at the same time, without losing his position.
It was a slow stop, at 8.7 seconds, and dropped him to ninth just as Vettel pitted again, taking his penalty before he rejoined fifth for the final charge. The Ferrari had made 12 places in 14 laps.
Defending champion Hamilton has 145 points after eight races.
Order had been restored by the 20th lap, with Hamilton's Mercedes ahead of the two Red Bulls and the two Ferraris.
Vettel lost fourth to Ricciardo on much fresher tyres through Le Beausset on lap 35 but out front, after the stops had shaken out, Hamilton was still solidly in the lead, five seconds clear of Verstappen and still 15 to the good on Vettel, who was struggling on his worn tyres which had taken a pounding as he came through the field. "It looks like we are chasing them this weekend".
By lap 23, Hamilton was in command ahead of Verstappen by six seconds with Ricciardo, Raikkonen and a charging Vettel, back up to fifth, leading the chase.