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First-half tries from Vincent Clerc and Maxime Medard opened a lead of 16 unanswered points as England shipped penalties and made basic errors across the park.
England struck back with a fine try from Ben Foden and closed to within seven points with three minutes left when Mark Cueto capitalised on a break from replacement Matt Banahan.
But they ran out of time and inspiration as Les Bleus set up a deserved semi-final clash with Wales.
France, so poor in their pool matches, were a side transformed as they took revenge for their World Cup defeats of 2007 and 2003.
"England were blown away in the first half and probably got a proper telling off. They came out with a little more pace and precision but they made too many mistakes with knock-ons, penalites and turnovers. England were never going to score from 80m out.
"Those who have watched England before could see they were not any different but whereas Scotland and Argentina couldn't last the distance and England won late on, France were a different outfit."
The defeat will leave manager Martin Johnson under pressure after his gamble of pairing Jonny Wilkinson and Toby Flood at 10 and 12 failed to ignite the England back line, while his forwards were repeatedly second best at the set-piece and in the loose.
Johnson's contract expires in November, and four weeks as memorable for scandals off the pitch as any achievements on it will do little to appease the notoriously twitchy committee-men at the Rugby Football Union.
France were supposedly a team in pieces, beaten by Tonga just a week ago and with coach Marc Lievremont publicly berating his players, but so clear-cut was their victory that much of the atmosphere had been sucked from the contest long before the end.
England had an early opportunity with a line-out deep in French territory after a clever grubber from Foden only for Lionel Nallet to burgle back possession, and they then tore into France again as Alexis Palisson was smashed backwards after taking a garryowen and Manu Tuilagi thundered into Morgan Parra.
After spluttering sporadically for four games, England's Kiwi campaign ended as it probably deserved to: in defeat, to a team that was more dynamic, more clinical and far more composed when it mattered most.
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But it was the most fleeting of false dawns. Dmitri Yachvilli slotted a penalty from distance after Flood failed to release his man on the deck, and France took a grip they would never relinquish.
Wilkinson was struggling, sending the re-start straight into touch and flinging a pass the same way, and France then went close to the first try of the contest as Clerc took a long pass out on the left and was just bundled into touch by the corner flag.
Yachvilli made it 6-0 with a second sweet strike from 45 metres after Matt Stevens was penalised for collapsing a scrum, and then slid another penalty just wide from the same spot.
England's players had talked of "blitzing" France in the first 20 minutes, but it was Lievremont's men with all the menace and danger.
Another line-out was stolen, and when the ball was sent left Clerc stepped and spun through limp challenges from Wilkinson, Chris Ashton and Foden to dive over and make it 11-0.
England were once again static in their few attacks, only Tuilagi's bullocking runs offering any threat, Flood reduced to aiming a long-range drop-goal pit which missed by a street.
Louis Deacon shipped another sloppy penalty, allowing Yachvili to kick to the corner, and after thunderous drives from the forwards left wing Alexis Palisson and Medard combined out wide to put the full-back in for France's second try.
England were in disarray, only Yachvili's failures with the conversions keeping them in the game, and when they finally created space for their wingers Cueto was dragged down metres from the line before another wayward pass from Wilkinson shut the door on Ashton wide out right.
England had never before come back to win from a margin of more than 12 points, and the errors continued to come thick and fast as Tom Croft became the latest to cough up the ball.
They grabbed an unlikely lifeline when Ben Youngs took a quick tap and go to release Foden, who jinked and dummied his way over to make it 16-5 with 23 minutes left on the clock, Wilkinson popping over the conversion for 16-7.
Johnson threw on his replacements but England kept wasting what good field possession they could work.
Flood popped out a careless off-load deep in the French 22 to allow a clearing kick to snuff out the danger, and when Nick Easter tried to rumble from deep within his own 22 his hospital pass to Tuilagi triggered another knock-on.
France, led by man-of-the-match Imanol Harinordoquy, set up camp in front of the English posts, and when the ball was fed back to Trinh-Duc the replacement fly-half slotted the drop-goal to make it 19-7.
Banahan's late charge allowed Cueto to touch down for a try at the death, but with Flood's conversion sliding wide England needed a converted try to force extra time - something they could neither conjure nor say their performance deserved.
England: Foden, Ashton, Tuilagi, Flood, Cueto, Wilkinson, Youngs, Stevens, Thompson, Cole, Deacon, Palmer, Croft, Moody, Easter.
Replacements: Wigglesworth for Wilkinson (65), Banahan for Youngs (65), Corbisiero for Stevens (49), Hartley for Thompson (56), Shaw for Deacon (49), Lawes for Croft (46), Haskell for Moody (63).
France: Medard, Clerc, Rougerie, Mermoz, Palisson, Parra, Yachvili, Poux, Servat, Mas, Pape, Nallet, Dusautoir, Bonnaire, Harinordoquy.
Replacements: Marty for Rougerie (68), Trinh-Duc for Yachvili (53), Barcella for Poux (56), Szarzewski for Servat (56), Pierre for Pape (65), Picamoles for Harinordoquy (72).
Not Used: Heymans.
England's World Cup dreams fell apart under a French onslaught on a night when their shortcomings were brutally exposed at the quarter-final stage.