Sale Sharks star Sebastien Chabal struck nine minutes from time, powering through weak English defence for the decisive score of a gripping game.
England's fifth successive home win under head coach Brian Ashton looked likely after Olly Barkley booted four penalties and Andy Gomarsall dropped a goal.
But 2007 World Cup hosts France, who claimed an early touchdown from veteran lock Fabien Pelous, struck a psychological blow ahead of a quickfire rematch in Marseille next Saturday.
Ashton will announce his 30-man World Cup squad next Tuesday and, despite the defeat, there were impressive contributions from fringe candidates Barkley and centre Jamie Noon.
Noon was a threat throughout the contest, defending tigerishly and attacking menace. Like Barkley, he might have done enough.
France, though, had just enough in the tank, as fly-half David Skrela and substitute scrum-half Jean-Baptiste Elissalde added 11 points with the boot.
England made 10 changes from the side that walloped Wales in record-breaking fashion last weekend as the countdown continued towards Ashton's World Cup squad unveiling.
There were first chances of the World Cup warm-up campaign for players like Barkley, Noon, Ben Kay and James Haskell, while France - whose World Cup 30 had already been announced by boss Bernard Laporte - played their first game since mid-June.
Wasps hooker Raphael Ibanez led the French, while Pelous won an 111th cap, equalling his country's Test record held by former Saracens centre Philippe Sella.
England, whose heavyweight pack power obliterated Wales, looked to leave an early impression, but they encountered a French side quick in thought and deed.
Wing Vincent Clerc displayed early signs of attacking menace and, after Barkley's opening penalty put England ahead, France struck.
England struggled to keep pace with French sleight of hand, and a crisp move ended with Pelous crashing over wide out, breaking wing Josh Lewsey's despairing tackle.
Skrela narrowly failed to land the touchline conversion, but France had provided England with more of a challenge in 15 minutes than Wales managed over 80 seven days earlier.
A 17th-minute Skrela penalty gave France breathing space, yet England roused themselves impressively, and Barkley's second penalty was followed by a thrilling midfield burst from Mike Catt the visitors only narrowly thwarted.
Some of England's close-quarter handling work matched French invention, and it had the feel of a proper Test match, despite the baking temperature which ensured another shirt-sleeved 60,000 Twickenham crowd.
Barkley completed his penalty hat-trick seven minutes before the break - French wing Aurelien Rougerie was punished for obstructing lively Newcastle centre Noon - and a one-point advantage rewarded England's unflinching commitment.
Hooker Mark Regan, though, lost his discipline as half-time approached, lunging recklessly at opposite number Ibanez.
Ibanez retaliated by throwing a haymaker - fortunately, it missed - but Regan's indiscretion was punished by Irish referee Alan Lewis, and Skrela slotted the simple penalty for an 11-9 advantage.
Barkley then had the final say of an absorbing opening 40 minutes, edging England one point clear through his fourth penalty and setting up a similarly exciting second period.
England defended admirably early in the second half, frustrating France, and they extended their lead when Gomarsall landed a drop-goal from short range following a sustained period of pressure.
Gomarsall's strike was the cue for a raft of substitutions on both sides as Phil Vickery, Martin Corry, Yannick Nyanga, Frederic Michalak and Chabal all entered the fray.
France cut the deficit to a point when Elissalde slotted a 35-metre penalty, taking the Test into its final quarter with England 15-14 ahead.
England's mighty fitness levels were underlined when they launched a scintillating attack on 68 minutes, and only a brilliant tackle by replacement French hooker Dimitri Szarzewski prevented one of Twickenham's great tries.
France, though, had no intention of playing second fiddle, and Chabal's brute strength - he smashed through attempted tackles by full-back Nick Abendanon and wing Josh Lewsey - harvested a 70th minute try which Elissalde converted.
Ashton's final throw of the dice saw Jonny Wilkinson replace Catt with two minutes left, yet not even their 2003 World Cup final matchwinner could rescue this one.