Ondrej Nemec led the way with two goals and an assist, and Vladimir Sobotka, Jaromir Jagr, and Roman Cervenka also scored for the Czechs in Thursday's triumph at the O2 Arena.
"I'm so happy we got three points, but now we have to get ready for tomorrow's game," said Nemec. The Czechs face Austria on Friday.
Kevin Hecquefeuille had the lone goal for France.
Goalie Ondrej Pavelec got the win without too much difficulty, as shots favored the Czechs 46-20. Battling to get to the quarter-finals, coach Vladimir Ruzicka's team is fourth in Group A behind Canada, Sweden, and Switzerland.
"They have a good defence," Czech captain Jakub Voracek said of the French. "We had a lot of chances, but we didn't score much until the third period. It's a big win. Ondrej made a couple of big saves when he had to."
Number one French goalie Cristobal Huet got the evening off, and Florian Hardy saw his first action of the tournament. Hardy was in net when France upset defending champion Russia 2-1 in 2013, but his best efforts weren't enough here.
There was plenty of other lineup juggling. In the wake of their 6-3 loss to Canada, the Czechs changed their defensive pairings, putting Jan Hejda with Michal Jordan and Nemec with Petr Caslava. Up front, Tomas Hertl joined the top line with Sobotka and Voracek, while Dominik Simon moved up to the second line with Jagr and Jan Kovar.
Jakub Klepis missed his second straight game with a hurt shoulder. Stephane Da Costa, who led France in assists (2) prior to this game, was also scratched due to an injury.
In the first period, the ice was tilted in the Czechs’ favor, as shots on net favored them 14-3, and Hardy had to be sharp. But even with a late-period hooking minor against French defenceman Jonathan Janil, the Czechs couldn’t cash in on the power play.
To the relief of the partisan crowd of 17,110, Nemec drew first blood at 1:10 of the second period when his rising shot from the right point eluded Hardy through traffic.
"On the first goal, I tried to shoot from the blue line, which is what the coaches have been telling us," said Nemec. "It's a good thing it went in."
The Czechs continued to press. Following a French turnover, Cervenka cruised in over the blue line and whizzed one off the crossbar.
At 6:58, Sobotka made it 2-0 with a screened slapper from the center point.
The French struck back just 1:43 later. An unguarded Hecquefueille took Loic Lamperier’s nice centering pass from behind the net and roofed it past Pavelec with bodies in front.
With seven minutes left in the middle frame, the crowd erupted with indignation after Nemec was crushed on a heavy Sacha Treille hit behind the Czech net. Though shaken up, he would continue.
"It seems at every World Championship I fall into the boards once," Nemec said. "Last year in Minsk, I fell like this against Italy. I was tired, and it was a long shift. Sacha Treille hit me, a clean hit, but I fell, and I couldn't breathe for a moment. If I score two goals like this, then I hope I fall every game!"
The Czech fans rose as one, bouncing up and down and chanting, willing their team to win. But it remained a one-goal game for a long stretch, and emotions ran high. Jagr and French agitator Antoine Roussel were sent off after a scrum in front of Hardy’s net.
Jagr got the crowd chanting his name early in the third when he nearly scored on a spin-around move on a partial break.
At 4:25 of the third period, Jagr gave the Czechs a 3-1 lead, tucking home the rebound from Jan Kovar's shot from the high slot after Hardy made a good blocker save. The legendary 43-year-old winger is the oldest player ever to score at an IIHF World Championship.
Hertl, after failing to convert on a breakaway, retrieved the puck behind the net and showed good patience before centering it to Nemec. He beat Hardy through the legs to make it 4-1 at 8:28.
"Tomas found me in front and I was alone in front of the net," said Nemec. "It was a lucky goal, but I'm happy I scored."
Cervenka added a little whipped cream to the Czech cake with 5:08 left, lifting a rebound home from the goal line to round out the scoring at 5-1.
"We knew we'd have to skate for 60 minutes, and I think that was the biggest difference," said Voracek. "We were skating in the third period. We continued to attack the net, and that's why we scored so many goals in the third."
France has never defeated the Czech Republic in seven all-time World Championship meetings. But it came close in Minsk last year, where a Jan Kolar overtime goal gave the Czechs a hard-fought 5-4 victory.
The French will battle Canada, whom they shocked in a shootout to open last year's tournament, on Saturday.