Scrum-half Greig Laidlaw was the star of the show for Scotland as they showed incredible spirit to come from behind in the second half.
France put the first points on the board when Teddy Thomas ran over with just two minutes on the clock and Les Bleus quickly moved into a 10-0 lead.
Sean Maitland did hit back for the hosts, however, Thomas again proved to be a nuisance when he latched on to his own kick to cross for the second time, and Maxime Machenaud's accurate boot put France 20-14 ahead at the break.
Laidlaw emerged as Scotland's hero in the second period, kicking six penalties, as they managed to hold France at bay to complete the turnaround and claim a 32-26 triumph.
"Playing in this jersey is unbelievable. It wasn't pretty at times but that's international rugby. I am so so proud of this team. We really dug in at the end and the forward pack in particular," Laidlaw said.
"It's felt like a long time coming back from injury and I'm not a very good watcher, so it's great to get back on this field, in this jersey and in front of this crowd."