A second half try from fullback Ben Foden proved decisive in a bruising encounter between the tournament's only unbeaten rivals, with Toby Flood and Jonny Wilkinson adding the rest of England's points from the boot.
Wilkinson's second-half penalty saw him surpass New Zealand's Dan Carter as international rugby's record pointscorer with 1 190 points.
France, who had beaten Scotland and Ireland in their opening two games, scored three penalties through scrum-half Dimitri Yachvili as England's defence held firm
An absorbing first half had finished level at 9-9, with Flood and Yachvili both contributing three penalties apiece after an error-strewn opening 40 minutes which finished with France on top.
England took the lead after only five minutes, when from the first scrum of the match France loosehead Thomas Domingo was penalised for collapsing.
Flood slotted the resultant penalty but France responded almost immediately with a penalty of their own, Yachvili converting from in front of the posts after Ashton went off his feet a ruck.
With England's forwards on top early on however, the home side's pressure began to tell and two more Flood penalties gave Johnson's men a useful six-point cushion.
Yet France hit back rapidly with two quick penalties from Yachvili to level the scores when Nick Easter and Tom Wood were pinged at the breakdown.
England then suffered a huge setback when giant loosehead Andrew Sheridan limped off with a leg injury, to be replaced by youngster Alex Corbisiero.
France were to dominate the remainder of the half, and only desperate English defence kept the visitors at bay.
England started the second half like men possessed and had France rocking from the restart, launching wave after wave of attacks.
France finally buckled when the ball was moved swiftly left and Foden powered through the cover to go over in the corner and make it 14-9. Flood missed with the conversion.
Moments later England thought they had landed a killer blow when clever inter-play between Flood and Ben Youngs sent Ashton clear to score under the posts only for play to be called back for a marginal forward pass.
Soon afterwards Flood was replaced by Wilkinson, whose first duty was to kick the penalty which saw him pass Carter as rugby's all-time leading points scorer to give England a 17-9 lead with 20 minutes to play.
France thought they had hit back when a grubber kick left England scrambling near the own line. But with a try begging, centre Aurelien Rougerie knocked on and England breathed again.