The French, now beaten in all three matches and propping up the table, gave a far better account of themselves at Twickenham than they had in their opening two games, and thanks to Wesley Fofana’s superb individual try took a 10-9 lead after the first half.
But their second-half substitutions disjointed them and the familiar mistakes returned.
Manu Tuilagi ran in a try after Owen Farrell had booted England ahead, and Toby Flood added another two penalties to make sure the match was safe.
England play Italy at home and then visit Wales on the final day – should they win both of those, they will win their first Grand Slam in a decade.
France, meanwhile, travel next to Ireland and are in danger of ending a tournament they began as favourites with the wooden spoon.
It took all of 44 seconds for France to give away a penalty, Yoann Maestri tackling from an offside position and Farrell kicking England into an early lead.
But this was not the same France side who had performed abysmally in defeats to Italy and Wales, and they looked the stronger and more determined in a scrappy first quarter.
Morgan Parra booted the visitors level soon afterwards as the match became a tetchy affair, with referee Craig Joubert struggling to set the scrum and Farrell involved on both ends of off-the-ball incidents.
England nudged back ahead via a penalty on 28 minutes, but a moment of inspiration from Fofana put the French in front for the first time.
The centre danced through a couple of lazy tackles from Chris Ashton and Ben Youngs, and ran in from almost halfway - evading no fewer than five England players by the time he touched down - with Parra adding the conversion from out wide.
But old habits die hard, and no sooner had France struck than Thomas Domingo gave away a sloppy penalty for not rolling away, meaning it was a one-point game at the interval.
France had their chances at the start of the second half too, but Parra shanked an early penalty wide, just as he had on the stroke of half time.
Farrell, by contrast, made it four from four to return England to the lead after 48 minutes.
The changes began from both coaches, but while the home side were rejuvenated, France lost their impetus.
And Tuilagi pounced, grabbing a loose ball after England caught Yannick Nyanga on his own with a high ball, and ran in at the corner.
Farrell missed the conversion, and another kick before going off with a groin injury on the hour.
But his replacement, Flood, ran the game well in the last quarter of an hour to close out the contest.
As the time dribbled away, so did France's ideas - replacement fly-half Frederic Michalak particularly culpable with some errant passes - and despite the result being clear, tempers flared in the final minutes.
Dan Cole was sent to the sin-bin and the final whistle came just as players from both sides had squared up to one another at the corner of the field.
The match against France had been billed ahead of the tournament as a possible title-decider, but it now looks more likely that particular showdown will be at the Millennium Stadium on March 16 when England meet Wales, who won earlier in the afternoon.
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