In a race with no retirements, Russell made overtaking manoeuvres late on against both Esteban Ocon in the Alpine and Yuki Tsunoda's AlphaTauri to provide Williams with its best result of the season.
The result was Russell's best finish for Williams since last season's Bahrain GP, while it also ensured the team is again ahead of Haas into ninth in the constructors' championship.
Despite challenging driving conditions with tyre degradation a key for strategy, Russell was able to excel at the Paul Ricard Circuit.
"It was really, really difficult from within," Russell told Sky Sports F1. "It was a really great race from within.
"Managing to do a couple of really nice overtakes, one with Tsunoda at the end which for us, finishing ahead of these cars, the Alfa [Romeo], Ocon, Tsunoda at the end, for us is massive.
"Finishing 12th on merit, I would go as far as saying it was our best ever race together.
"It is a shame nothing happened in front because as I say, 12th on merit is ordinarily quite a good result but nevertheless, really pleased with that and a good way to start the three weeks."
Russell looking to improve race starts
Russell prospered throughout his junior category career but since joining the back-of-the-grid Williams team, the British driver has struggled to perfect his first-lap performances.
It was a similar story at Paul Ricard, with Russell explaining: "I didn't do enough of a job at getting the tyres in the window on the formation lap and I just had a load of wheelspin off the line and it is just a knock-on effect.
"I got sandwiched into turn one, had a car on the outside, a car on the inside and there was nowhere I could go.
"It is something I have really struggled on since I have been in F1 to be honest. Since I have been at the back of the grid, I really need to work on it.
"We keep on trying but we managed to make it work in the end, pitting early and took those hards a really long way."
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