Scotland celebrated two tries in Paris as they sought a first win there since 1999
Scotland were expected to struggle with France's physicality and so it proved as Vern Cotter's side found themselves on the back foot immediately.
With the Paris crowd baying for blood, the French could only land minor blows and a dominant first 15 minutes only heralded three points from the boot of Camille Lopez.
And having weathered the storm, Scotland took the lead through Stuart Hogg's third try of the championship, converting a two-on-one in the right corner to the joy of a strong travelling support.
France dominated at scrum time as they were expected to do
Greig Laidlaw went off in the first half, a massive blow for Scotland's hopes
Greig Laidlaw's conversion was uncharacteristically short, bouncing off the crossbar, and he would not score a point in the game.
The Scottish captain was forced off before the break with an ankle injury that saw him on the sidelines in a "moon boot" for the rest of the game, an injury that Cotter will be desperate for his skipper to overcome.
France started to make their dominance pay, Gael Fickou ducking under Hogg's tackle to finish a frenetic period of rugby from the home side.
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Lopez slotted a fine touchline conversion to leave trailing 13-5 and without their goal-kicker and captain.
However, fly-half Finn Russell stepped into the breach and slotted two penalties to reduce the deficit to just two at half-time.
Further injuries to John Barclay and John Hardie in the back row left Scotland reshuffling just after the break, with second row Tim Swinson deputising at flanker.
And it proved to be an inspired switch, Tommy Seymour gathering his own chip before finding Swinson who crossed under the posts for his first international try.
Russell was hurried by the referee and kicked under the crossbar as the ball fell off the tee in what must go down as one of the worst conversion attempts in Six Nations history.
The game slowed as the sheer physicality of the French pack led to multiple stoppages for head injury assessments and Scotland were forced to use their bench far earlier than they would have hoped.
Remi Lamerat thought he had scored France's second try after they shunned a simple penalty in favour of a scrum, but the TMO ruled it a knock-on as he reached for the line with 12 minutes left.
Scotland won a rare penalty at the scrum to allow them some respite but France eventually managed to take the lead, Lopez slotting over from nearly 50 metres to take a 19-16 lead – the same scoreline by which they had lost in London a week previously.
But their continued dominance at the scrum allowed them to pin Scotland back and another Lopez penalty completed the victory.
The visitors can take little from the game but the new scoring system means they were at least able to take a point by virtue of avoiding defeat by more than seven points.