Les Bleus, who had lost nine of their last 11 meetings against England in the Championship, prevailed through penalties by Maxime Machenaud (4) and Lionel Beauxis and a penalty try while their opponents scored two penalties and conversion by Owen Farrell, a penalty by Elliot Daly and a try by Jonny May.
Ireland top the table with 19 points from four games after securing a 28-8 bonus-point victory over Scotland earlier on Saturday, meaning they cannot be caught by England when the two teams meet at Twickenham next weekend.
France, who narrowly lost their first two matches against Ireland and Scotland, defended furiously throughout and it became obvious that England, who needed a bonus-point win to keep their title hopes alive, would not score the four tries they needed.
It was England's second defeat in a row after they lost to Scotland in the previous round of matches and only their third in 27 matches under coach Eddie Jones.
France collapsed the scrum early on and Farrell, captain in the absence of the injured Dylan Hartley, converted the resulting penalty.
England enjoyed possession but could not find a way through a solid French defence.
The visitors, however, pinched three French lineouts in a row to continue their domination, although the hosts threatened after Remy Grosso ran 40 metres after stealing the ball in his 22 metres.
England struggled at the breakdown but Daly landed a 53-metre penalty to double their advantage midway through the first half.
Number eight Nathan Hughes was carried off the pitch with a leg injury and was replaced by Sam Simmonds as Machenaud converted his first penalty attempt, only for Farrell to restore a six-point advantage as France were penalised for collapsing a maul.
France piled the pressure in England's 22 but were only rewarded with a penalty after a dangerous tackle.
Machenaud slotted it home and levelled with a 45-metre kick after England were penalised for offside shortly before halftime.
Nine minutes into the second half, the crowd went into raptures when France were handed a penalty try after Benjamin Fall was tackled high by Anthony Watson after collecting a superb kick to the corner by Machenaud.
Watson picked up a yellow card for his dangerous tackle and Les Bleus came close to scoring another try but England held them over the line at the end of a lightning-quick counter- attack.
Machenaud converted another penalty as France extended their lead to 10 points but the visitors reduced the arrears six minutes from time when May touched down in the corner after England stole yet another French line-out.
But replacement flyhalf Beauxis converted a routine penalty to give France breathing space with two minutes left and the home side survived a late onslaught to beat England for the first time since 2015.
(Reporting by Julien Pretot; Editing by Ed Osmond)
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