Maxime Machenaud kicked the resulting conversion from under the posts as an exhilarating contest ended in fitting style with France beating their fiercest rivals for the first time since the 2011 World Cup quarter-finals.
France looked to have blown it after two Yoann Huget tries had given them a 16-3 lead midway through the first half, only for Mike Brown — with his first try in 22 England matches — and Luther Burrell, on his debut, to cross the white wash and help England to a five-point lead with just three minutes left.
In the build-up France coach Philippe Saint-Andre laughed off suggestions his team were favourites for the championship, given they finished last in a miserable 2013 in which they lost eight out of 11 matches.
Yet this win will add weight to the suggestion that Les Bleus are favourites in a post-British and Irish Lions tour year, having won the championship on the last four such occasions.
England's other debutant, wing Jack Nowell made a disastrous start as France opened the scoring after just 32 seconds.
Nowell dropped the kick-off from France's own debutant Jules Plisson and the French were quick to strike as Plisson's deflected kick ahead deceived Brown, allowing Huget to take the ball in his stride and dive over in the corner.
Scrum-half Jean-Marc Doussain missed the conversion and on six minutes Owen Farrell kicked a penalty after France were penalised for not rolling away to bring the score back to 5-3.
A penalty from Doussain on 11 minutes extended France's lead before Huget scored again on 16 minutes.
Tom Wood lost the ball in the tackle and France struck with lightning efficiency, going wide right where Huget took on Goode on the outside and fed Brice Dulin inside.
His chip ahead bounced awkwardly, deceiving Nowell and Goode before dropping into Huget's arms to score in the corner again.
Doussain missed the conversion but kicked his second penalty on 23 minutes and France led 16-3.
England were struggling to get into the match but did have their chances, although Goode spilled the ball five yards from the line after a clever break down the blindside.
England refocussed on their strengths and battered away at the French defence with their forwards before a quick tap penalty from a kickable position by scrum-half Danny Care took England to within sight of the tryline.
The ball was sent left and Brown stepped inside Huget and held off tackles from locks Pascal Pape and Alexandre Flanquart to touch down, although Farrell missed the extras.
That changed the momentum of the match and England finished the half banging on the door, although Farrell missed a drop-goal attempt.
They came out firing after the break and another dart from Care saw him held up an inch short of the line, but Farrell landed a penalty to cut the deficit to 16-11.
The worm had well and truly turned and Billy Vunipola powered through the midfield before off-loading to debutant Burrell, who scored under the posts.
Farrell's conversion gave the visitors an 18-16 lead.
Care, who was having a magnificent match, then nonchalantly dinked over a drop goal from under the posts on 57 minutes.
England had been bossing the second half but France piled on the pressure at the scrum, where they had already forced two penalties, and a third allowed replacement scrum-half Machenaud to kick them back to within two points.
Yet an immediate reply from Goode, as Farrell was down receiving treatment for cramp, saw England open up a 24-19 lead.
But Fickou had the last say as Nyanga made another marauding break down the right before France switched the ball to the left and Dimitri Szarzewski fixed
Burrell before passing to Fickou who dummied a pass to Medard before darting inside Goode to run in under the posts.