The Mercedes driver saw off his team-mate by 0.335 seconds at the Paul Ricard Circuit.
Championship leader Max Verstappen finished third for Red Bull one place ahead of Sergio Perez winner of the Azerbaijan Grand Prix earlier this month.
Bottas arrived in the south of France as a man under pressure following a lacklustre display in Baku, where he started only 10th and finished 12th.
But his opening salvo of the weekend will provide him with a much-needed boost of confidence heading into the remainder of the seventh round of the campaign.
The Finn is already 57 points behind Verstappen in the standings, with Englishman George Russell waiting in the wings for a seat at Mercedes next year.
However, it was not a session without incident for Bottas after he sustained damage to the floor of his Mercedes by running over the rumble strips at Turn 2.
Mercedes team manager Ron Meadows expressed his anger at the incident to FIA race director Michael Masi, claiming it could cost his team a six-figure bill.
Bottas’ team-mate Hamilton is four points adrift of Verstappen but following two off-colour weekends in Monaco and Azerbaijan, the British driver’s Mercedes team appear better placed to take the fight to Red Bull.
Indeed, Verstappen finished almost half-a-second adrift of Bottas in the opening hour, with Perez, who took advantage of his team-mate’s tyre blowout in Baku to claim his maiden win for Red Bull, seven tenths back.
Aston Martin’s Sebastian Vettel ran into the barriers at the fast-sweeping Turn 11 but was able to limp back to the pits for repairs. Ferrari’s Carlos Sainz and Haas driver Mick Schumacher also suffered spins on Formula One’s return to Le Castellet after last year’s round was cancelled due to Covid-19.
Esteban Ocon, who earlier this week agreed a three-year extension with Alpine, finished fifth ahead of McLaren’s Daniel Ricciardo, with double world champion Fernando Alonso seventh.
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