"When I'm 60 I'll tell my grandchildren that I was captain of the team that beat Russia at the world championships," a beaming Vincent Bachet told reporters.
All the scoring came in a see-saw second period, with Damien Fleury and Antoine Roussel notching the vital goals for France after Alexander Perezhogin gave Russia the lead. Alexander Radulov also missed a penalty for the Russians.
The defending champions turned up the heat in the final period but, even with a frenzied offensive effort in the final minutes, the Russians could not find a way through the massed ranks of the French defence.
Despite taking 29 shots to France's 19, Russia came off second best and their unbeaten streak at the world championships ended at 13 games.
In the late game in Helsinki, Martins Cipulis scored after just 15 seconds to put Latvia on the road to a 5-3 win over Slovakia, their first victory of the tournament.
Canadian goalkeeper Mike Smith was the hero in Stockholm, stopping 33 shots to shut out co-hosts Sweden as his side cruised to a 3-0 victory.
The Czech Republic defeated Denmark 2-1 in a shootout after a goal for each side from Zbynek Michalek and Morten Poulsen in the third period forced overtime in the early game in Sweden.
Switzerland remain top of the Stockholm group on 11 points from four matches, ahead of Canada (10), Sweden (9) and Norway (6).
Despite their defeat, Russia maintain their position as leaders of the Helsinki group on goal difference, level on nine points with the United States. Hosts Finland are third with eight with Slovakia in fourth place on six points.
The top four teams in each eight-team group go through to the quarter-finals.
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