After denying Wales the Grand Slam with a thrilling last-gasp home win on Super Saturday, Les Bleus needed to secure a bonus-point triumph at a wet Stade de France and also win by a 21-point margin to claim a first championship since 2010.
However, instead Duhan van der Merwe’s dramatic try at the death sealed a first victory for Scotland - who had fly-half Finn Russell sent off in the closing stages and also saw captain Stuart Hogg yellow carded before half-time - in the French capital since 1999.
“What a tournament it has been and, from a Welsh point of view, we are over the moon,” Wales head coach Wayne Pivac, whose team will be presented with the trophy on Saturday, told the BBC.
“We are very happy to have won the championship.
“It’s a shame we couldn’t have done it together as a group last week. We felt we did quite a bit in the game to win it but it wasn’t to be.
“It doesn’t take away from the fact a lot of hard work has been done and we’ve come out on top of the points table and won the tournament.
“Some great rugby has been played in this tournament and it is exciting times for all concerned.”
Romain Ntamack - starting in place of the injured Matthieu Jalibert - had France in front early from the tee, but, no doubt with that big points target in mind, they were initially guilty of overplaying at every opportunity as Scotland applied plenty of pressure.
South Africa-born wing Van der Merwe went over for his first try of the night amid suspicions of a double movement and Russell then made the Scottish lead seven points before France began to get a grip on the occasion and Ntamack cut the advantage with another penalty.
Scotland were conceding multiple penalties as they came under enormous pressure inside their own 22, with full-back Brice Dulin eventually finishing after Van der Merwe had missed a tackle on Damian Penaud following Antoine Dupont’s looping pass out to the right flank.
Hogg paid the price for Scotland’s persistent offending before France botched a key lineout chance on the stroke of half-time.
Scotland defended hardily with 14 men, but were undone by a sublime chip-and-chase from the fleet-footed Penaud.
Ntamack couldn’t nail a difficult conversion and Russell failed with an ambitious drop-goal attempt before he did then pull his side back within five points with a simple penalty.
Scotland went back in front courtesy of a third try in two matches from replacement hooker Dave Cherry, who reacted quickest after a rip from French lock Swan Rebbadj. The score was given after a lengthy TMO check.
Now the talk was less about whether France could claim the title and more regarding if Scotland could finally end their Paris hoodoo.
A combination of Rebbadj’s close-range score and Russell’s dismissal for an arm to the neck of Dulin appeared to scupper those chances, before a swift yellow for French substitute scrum-half Baptiste Serin levelled the numbers.
Then ensued a truly dramatic ending, with France made to pay for trying to launch one last attack as Scotland maintained their discipline with the clock in the red and Van der Merwe completed his brace in stunning fashion after cutting inside following a long pass from Adam Hastings.
The win wasn’t enough to move Scotland out of fourth place - an eight-point victory would have seen them claim a Six Nations-era highest finish of second spot - but nevertheless a jubilant end to an eventful campaign that featured victories in London and Paris for the first time since 1926.
Meanwhile, despair for France after their second successive Six Nations near-miss. Their wait for another title will enter a 12th year.
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