Scott Johnson's men scored twice in the first half through Stuart Hogg and Tommy Seymour to leave the championship chasers shocked at the break.
But an error from Duncan Weir - the Scots' matchwinner in Rome two weeks earlier - let in Yoann Huget to score just as the Scots looked like they were ready to build on their lead.
Weir did nail a nerveless penalty to put Scotland back ahead but Doussain's late kick and 11 points from the boot of scrum-half Maxime Machenaud handed Philipe Saint Andre's team their third win of the tournament.
Scotland had picked up their first win of the campaign in Italy when Weir scored a last-gasp drop-goal - but this time it was the Dark Blues who suffered late agony.
However, they at least showed signs that they have moved on from their 20-0 humiliation at the hands of England the last time they ran out in Edinburgh.
Skipper Kelly Brown was back in the team after being cast aside after a dismal display in the tournament opener and was joined by prop Geoff Cross and David Denton.
But it was Cross who failed to handle Thomas Domingo's early pressure as he buckled at the first scrum contest just two minutes in.
Machenaud took advantage as he slotted over an easy penalty, before doing the same just moments later as the Scots were forced to foul at the breakdown in a bid to halt a rampant French breakaway.
But Les Bleus scored the rugby equivalent of an own goal to hand Scotland the opening try after 11 minutes. Hogg sent an up-and-under beyond the posts but Huget and Brice Dulin collided as they both went to collect the high ball and Hogg darted in to apply the touchdown to the loose ball.
Referee Chris Pollock had to send the decision upstairs to the TMO but after a short delay he got the okay to signal a huge cheer from the home supporters.
Greig Laidlaw added the extras to put the hosts ahead, but Les Bleus responded through another Machenaud penalty.
Scotland have shaken off the wounds sustained in that meek surrender to the Auld Enemy, though, responding to that minor setback in stunning style.
After powering to within 10 yards of the French line, they tugged their opponents one way then the other with a rapid three-man move involving Weir, Matt Scott and finally Seymour, who found a small gap to dart through for their second score.
Laidlaw again did the necessary with the conversion but Hogg failed with an ambitious 45-yard drop-goal attempt five minutes before the break while Machenaud also missed a penalty attempt on the stroke of half-time.
Scotland started the second half determined to build on their lead but were let down by their Rome hero after 47 minutes.
After his pack had done brilliantly to turn the ball over deep in French territory, Weir suffered a rush of the blood to the head as he tried an ambitious pass to Alex Dunbar, only to see Huget intercept.
It was a cruel blow for the 22-year-old as he was forced to watch the Stade Toulousain wing dart 80 yards upfield to score under the posts, with Machenaud adding the simplest of conversions.
Laidlaw came-up short with a 40-yard penalty attempt on the hour mark but there were at least no signs that France were ready to streak away to an easy win.
Weir made amends for his earlier blunder as he floated over a perfect penalty after taking over kicking duties from Laidlaw to nudge his side back in front.
France were desperate for a score but with Ross Ford on for Scott Lawson at hooker, the Scottish scrum looked rock solid.
And it was from another dominant heave five minutes from time that the French pack collapsed, handing Weir a chance from almost halfway.
However, he could not repeat his match-winning act from the Eternal City and watched in horror as his kick came down before the posts.
Scotland had just a single point lead as the clock ticked down and needed to keep their discipline.
But lock Tim Swinson's failure to release at the breakdown handed France a simple kick in front of the posts and Doussain won it for the visitors, with no time left for a Scottish response.