Inspired by the recalled veteran Mike Catt, who was named as captain for the day, the English prevented the French from scoring a try and ran in two of their own.
The world champions were without Jonny Wilkinson but his replacements, Toby Flood and Shane Geraghty, proved to be inspirational understudies.
Flood scored the first try and kicked 11 points in his first start for his country while Geraghty produced a great break for Mike Tindall's match winning try 10 minutes after coming on as a replacement for his international debut.
France, the defending Six Nations champions, were strangely subdued and were only able to remain in contention for as long they did because of a series of English errors.
They led 12-9 after a disjointed first half. Three penalties from David Skrela and and one for Dimitri Yachvili gave them a three-point advantage.
Flood kicked three penalties and missed two for England.
Eight minutes into the second half England were rewarded for their greater ambition and as the ball moved to Catt who defied his 35 years with an explosive 10-metre burst and managed to unload in the tackle for Flood, who ran round under the posts and then converted his try.
France responded strongly with Serge Betsen at the heart of their attacks but although two more Yachvili penalties regained the lead after an hour, they showed little invention.
|England's Josh Lewsey gets plenty of encouragement [Reuters]|
Flood then went off with a dead leg to open the way for Geraghty and the 20-year-old was immediately involved with two ambitious unloads and then a penalty in the 68th minute to restore England's lead.
Geraghty made an even greater impact in the 73rd minute with a searing break to set up Tindall for the decisive score.
England, who have finished fourth, fourth and third since winning the world cup now have a chance of winning the title for the first time since 2003.
But Brian Ashton, the England coach, warned his rebuilding programme still had a long way to go.
"This is a one-off game," he told reporters. "We've got to back up performances like this and we've got to become consistent in playing that sort of game.
"Whilst it's great to get a win under our belt, we know there are areas of the game that we've got to work on."
France remain favourites to retain the title, but know they have much to do if they are to challenge the likes of New Zealand and South Africa for the World Cup later this year on home soil.
"We were not ambitious enough," said their coach Bernard Laporte. "We should have scored twice in the first half, we allowed them to come back into the game three or four times.
"We played well defensively but not in attack."
The result sets up the Six Nations for a grand finale on Saturday, with three teams, England, France and Ireland all on three wins and all in with a chance of taking the title.
The final weekend of the tournament will see England visit Wales while France are at home to Scotland and Ireland travel to face Italy.