Had reigning champions France recorded their fourth straight bonus-point win of this season's Championship, they would have wrapped up back-to-back titles.
But Scotland ran in seven tries as they posted their highest score against France, who managed six tries of their own in an enthralling contest.
Both France and Scotland now have 16 points heading into next weekend's 'Super Saturday' round of concluding fixtures.
France will retain their title by achieving a better result against England in Paris than Scotland manage against Ireland in Dublin -- unless both lose and Ireland sneak past to win the Six Nations instead.
Significantly, France's match kicks off several hours after the Ireland-Scotland encounter, so Les Bleus will know exactly what they need to do to be crowned champions.