The four-time world champion's lap of 1 minute, 30.029 seconds around Paul Ricard was enough to edge out teammate Valtteri Bottas to ensure he starts from the front in Sunday's race.
He later added: "I feel very grateful, grateful for a solid weekend".
Deposed championship leader Sebastian Vettel, meanwhile, endured a nightmare race as he crashed into the Mercedes of Valtteri Bottas at the first corner. "In the end with P3 I'm happy because the vehicle should be good in the race".
Vettel, at the back after a pit stop to fix the front wing damaged in the crash with Bottas made light work of the backmarkers, starting with a light tap as he passed Fernando Alonso's McLaren at Turn Three at the re-start, which nudged the Spaniard into a spin.
"Great work guys I am so happy for England", said Hamilton.
Forecasts of rain never materialised in Le Castellet, but a couple of collisions - one of which ruled home hopes Pierre Gasly and Esteban Ocon out of the remainder - on a dramatic first lap led to the safety auto being deployed.
Martin Brundle: "I sometimes think that Lewis thinks "right, I'm going to have to get on with this now" and he just cleans up when he is fully engaged".
Race officials reviewed the incident and gave Vettel a five-second time penalty.
Speaking to Sky Sports F1, Verstappen said: "We are all human".
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Trump quickly retweeted at least a half dozen posts about the report from the "Fox & Friends" morning show on Fox News Channel. Then he turned to other reporters and went over the same list for another 20 minutes.
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Alonso won the last of his two championships back in 2006, but here Hamilton has taken a big step to claiming his fourth title in five years, and his fifth in all.
Raikkonen himself did little to dampen the speculation on track, lapping over a second shy of Hamilton and in excess of half a second behind Vettel.
Moments later there was more trouble when Pierre Gasly ran his Toro Rosso into the back of Esteban Ocon's Force India, knocking them both out of the race and bringing out the safety vehicle. Mercedes kept Hamilton out until lap 33 when he stopped for the soft tyres, emerging behind Raikkonen who had yet to stop. Ricciardo was not as lucky with his stop in the 29th lap as Vettel raced by him into fourth.
Verstappen pitted in the 26th lap and came out just ahead of Vettel.
Vettel showed no signs of damage, and began his charge back through the field.
Both had gained an extra position in the last three laps, as Renault's Carlos Sainz Jr slipped from sixth to eighth reporting "no power".
A flying late lap by Leclerc lifted him to 10th for Sauber, pushing Esteban Ocon and his Force India team-mate Sergio Perez out of the shootout in 11th and 13th, either side of Nico Hulkenberg of Renault.
McLaren still fared better than former champions Williams, who had Russian Sergey Sirotkin 19th and Canadian Lance Stroll 20th.
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