Wales clinched the Six Nations as 14-man Scotland snatched their first victory in Paris since 1999 to wreck France's title hopes.
Damian Penaud's second-half score showed France's danger, but they could never stretch clear of their visitors.
Scotland's Finn Russell was shown a late red but Duhan van der Merwe swooped for a decisive late try.
It was fitting that a Championship that has been packed with tight games and show-stopping finales should finish with another match-deciding score and the clock deep in the red.
As Scotland's players leapt skywards to celebrate Van der Merwe's step and finish, France's slumped to the sodden Stade de France turf.
However, their hopes of swiping the trophy from Wales had long since gone.
It is the sixth title of the Six Nations era for a Wales side that came into the campaign as distinct underdogs after an underwhelming autumn.
France: Dulin; Penaud, Vakatawa, Vincent, Fickou; Ntamack, Dupont, Baille, Marchand, Haouas, Le Roux, Rebbadj, Jelonch, Ollivon, Alldritt.
Replacements: Thomas for Vakatawa (61), Serin for Dupont (64), Gros for Baille (56), Chat for Marchand (56), Atonio for Haouas (60), Taofifenua for Le Roux (50), Cretin for Jelonch (63).
Not Used: Bouthier.
Sin bin: Serin (73).
Scotland: Hogg; D Graham, Harris, Johnson, Van der Merwe; Russell, Price, Sutherland, Turner, Z Fagerson, Skinner, Gilchrist, Ritchie, Watson, Haining.
Replacements: Jones for D Graham (66), Hastings for Johnson (73), Kebble for Sutherland (49), Cherry for Turner (59), Craig for Skinner (75), Wilson for Haining (67).
Not Used: Berghan, Steele.