The Mercedes star has leapfrogged Sebastian Vettel who was holding onto a narrow lead in the points table.
The final moments of qualifying became a duel between the Mercedes drivers, with Bottas going top just before Hamilton crossed the line with the leading time for his third pole of the season.
Hamilton will lead the sport's return to France as the Paul Ricard circuit plays host to its first race since 1990, and the country's first grand prix in a decade.
"I feel very grateful for a solid weekend", said Hamilton after his victory at the Circuit Paul Ricard, the first French GP in 10 years.
JCB Head of Sponsorship Edd Hood said: "The JCB brand has a strong reputation throughout Europe and, with our Williams Martini Racing partnership, a great understanding of the demands of Formula One so it makes flawless sense for us to provide this professional trackside back up service".
"This place is attractive, it's really stunning down here", Hamilton said of a circuit that last hosted a grand prix in 1990 and represents a new challenge for a man who has won everywhere else on the calendar.
The German manufacturer meant to bring an upgraded version of its engine to the previous race in Montreal but delayed it because of a last-minute reliability concern.
"My start was too good and then I ended up with nowhere to go", he said to journalists in the paddock.
France's most recent grand prix was at Magny-Cours in 2008, the year Hamilton won his first world championship with McLaren, and it remains a rare country that has yet to see the Mercedes driver triumph. We had a good auto in the race, but the outcome was not what we wanted.
The session had one red flag near the end when Marcus Ericsson spun out of control and slammed into the barrier on Turn 11. Toro Rosso's Brendon Hartley wedged between the two McLarens and was 17th fastest.