The victory was Australian coach Eddie Jones’ fifth straight win since taking over from Stuart Lancaster, the English having seen off Scotland (15-9), Italy (40-9), Ireland (21-10) and Wales (25-21).
It was England’s first Grand Slam since their World Cup-winning year of 2003, when Jones was in charge of losing finalists Australia.
But it was not easy going at the Stade de France for England, who scored three tries through Danny Care, Dan Cole and Anthony Watson with Owen Farrell contributing 16 points with the boot.
A rash of ruck infringements allowed France to keep in the game through scrum-half Maxime Machenaud, who booted seven penalties in a flawless kicking display.
Machenaud got the scoreboard rolling after Maro Itoje was pinged at a ruck, but Farrell responded immediately when France skipper Guilhem Guirado was penalised for a dangerous tackle.
France delighted a packed stadium by running the ball with intent, Scott Spedding and Virimi Vakatawa, born in South Africa and Fiji respectively, both splitting the English defence only for final passes to go amiss.
Livewire scrum-half Care, who dictated a fast pace, showed up some lax ruck defence by stepping straight through a gap left by lumbering prop Jefferson Poirot and crossing for a well-taken try, converted by Farrell.
France suffered a blow when Francois Trinh-Duc limped off after 13 minutes to be replaced by Jules Plisson at fly-half.
Spedding broke through again, with France finally showing their attacking muster after generally failing to fire in tight wins over Italy (23-21) and Ireland (10-9) and defeats by Wales (19-10) and Scotland (29-18).
Machenaud booted his second penalty, but England again came firing back up the pitch, prop Cole bundling over the line for a try Farrell again converted.
England, with Billy Vunipola and flanker James Haskell to the fore, denied wave after wave of home attack, Machenaud keeping France in the game with a third penalty after another ruck infringement.
It was then France’s turn to defend and they did so with aplomb as Care marshalled his team from left to right, before two knock-ons undid English efforts.
Machenaud knocked over a fourth penalty to leave the score 17-12 at half-time with Farrell missing his second effort.
The first match of Saturday’s final day of the Championship was over as a contest before half-time with Wales 27-0 up at the break following tries by Rhys Webb, Dan Biggar and Jonathan Davies.
Six more tries followed after the break, with replacement Ross Moriarty scoring twice.
Both the final score and their 53-point margin of victory saw Wales surpass their previous bests against Italy achieved in a 61-20 win in Rome last year.
Wales have been criticised for a grinding approach, even when winning this tournament.
But there was nothing sluggish about their start on Saturday, with Webb scoring in the fourth minute.
Jamie Roberts charged through midfield and a chip over the top led to a Welsh line-out close to Italy’s line.
Webb, making his first Wales start since September after he missed last year’s World Cup with a foot injury, broke off the back of an ensuing maul and found a gap in the visitors’ defence.
Fly-half Biggar converted and then extended Wales’s lead with a penalty.
Italy then avoided conceding another try but at the cost of scrum-half Guglielmo Palazanni being sent to the sin-bin by French referee Romain Poite after he prevented Webb taking a quick tap penalty.
Biggar landed the easy kick and Wales led 13-0, with Italy a man down.
Wales continued to attack but handling errors and a penchant for the floated pass scuppered potential try-scoring moves before a successful exchange between Biggar and centre Roberts in the face of weak tackling sent the outside-half in between the posts.
Biggar duly converted, but at 20-0 to Wales, after just 29 minutes, the match had the feel of a training session rather than an international.
Minutes later, Wales had their third converted try and best of the half.
Powerful wing North broke clear from deep in the Welsh 22 and passed infield to Biggar who, with the Italian defence in retreat, sent in onrushing centre Jonathan Davies.
Roberts went in at the corner early in the second half with Biggar, for once, missing the conversion, although Wales were now 32-0 ahead.
The imposing North had Wales’s fifth try when his break and swerving run from halfway saw him surge past Italy replacement Luke McLean and through a non-existent defence.
Italy avoided being ‘nilled’ with Palazanni going over following a close-range line-out.
But barely a minute later Wales had their sixth try when Roberts and Davies combined to set up full-back Liam Williams.
Italy centre Gonzalo Garcia then crossed for a converted try only for Wales to respond through Moriarty.
It looked as if Odiete had scored a late intercept try that saw him run the length of the field but he was called back for offside.
As Odiete retreated, a quick tap sent in Moriarty before, in the final minute, replacement Gareth Davies scored Wales’s ninth try.
England travel to France in search of a first Grand Slam in 13 years and in their way stand a France side who will provide formidable opponents in Paris.
Dubai-based residents from each country are on hand to provide a preview of each team ahead of ‘le crunch’.
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MARC BENOISTE (ABU DHABI FRENCH) – FRANCE
THOUGHTS: England may have a Grand Slam in the bag but will still fear travelling to France as there is no team that Les Bleus would rather beat more, regardless of the situation.
I expect France to stick to their usual gameplan of wearing down the opposition with brute physicality before trying to release their dangerous backs, roared on by a partisan home crowd. If England can weather an early onslaught then they will feel confident of winning, but with so much on the line, I have no doubt that France will produce their best performance of the tournament.
FRANCE LINE-UP: 15-Scott Spedding, 14-Wesley Fofana, 13-Gael Fickou, 12-Maxime Mermoz, 11-Virimi Vakatawa, 10-Francois Trinh-Duc, 9-Maxime Machenaud; 1-Jefferson Poirot, 2-Guilhem Guirado (captain), 3-Rabah Slimani, 4-Alexandre Flanquart, 5-Yoann Maestri, 6-Damien Chouly, 7-Bernard Le Roux, 8-Loann Goujon
PREDICTION: France to win 20-18.
BEN ROTHWELL (DUBAI WASPS) – ENGLAND
ENGLAND LINE-UP: 15-Mike Brown, 14-Anthony Watson, 13-Jonathan Joseph, 12-Owen Farrell, 11-Jack Nowell,10-George Ford, 9-Danny Care; 1-Mako Vunipola, 2-Dylan Hartley (captain), 3-Dan Cole, 4-Maro Itoje, 5-George Kruis, 6-Chris Robshaw, 7-James Haskell, 8-Billy Vunipola
PREDICTION: 36-21 to England.