The hosts, who were 21-3 down at halftime after being blown away by an electric French team and had Zander Fagerson sent off after the break, prevailed with tries by Darcy Graham, Pierre Schoeman and Dave Cherry as captain Finn Russell kicked 10 points.
France, in their first World Cup preparation game, scored through tries by stand-in scrumhalf Baptiste Couilloud, debutant Louis Bielle-Biarrey and Cameron Woki with the rest of the points coming from the boot of Mathieu Jalibert.
France and Scotland, who lost Ben White to a possible ankle injury, will meet again in St Etienne next Saturday.
"We had a very very good first half and in the second half we made a few errors while we did not convert a handful of opportunities. It's frustrating that we did not win," France captain Brice Dulin said.
While Greg Towsend picked a side who could start against South Africa in the World Cup on September 10th, Fabien Galthie fielded three debutants and notably rested scrumhalf Antoine Dupont and flyhalf Romain Ntamack with most of the team having not played for France in over a year.
Scotland were first on the scoreboard with a Russell penalty, but were then completely outplayed by Les Bleus, who scored their first try when Couilloud finished off a brilliant combination on the right flank by Bielle-Biarrey and Emilien Gailleton.
Bielle-Biarrey was at it again to dive over for France's second try after evading Hamish Watson's tackle.
Things got worse for Scotland when White was taken off seven minutes from the break and headed into the dressing room with his lower leg wrapped in ice.
Galthie's side put the hammer down on the stroke of halftime as Woki crashed over the line to complete some good ground work by the forwards.
The hosts finally entered the contest in the second half, with Graham beating Ethan Dumortier to Russell's kick to reduce the arrears, cutting France's lead down to 11 points after the conversion.
Fagerson picked up a yellow card for striking Pierre Bourgarit in the face in the 51st minute and it was upgraded to a red four minutes later.
Scotland had the momentum, however, as Schoeman dived over before Russell converted to reduce the gap to four points.
Galtier made six changes within 10 minutes but it did not help.
Blair Kinghorn knocked the ball down in the corner for what Scotland thought was their third try, only for referee Ben O'Keeffe to rule it out for a Graham knock-on in the build-up.
The try came shortly afterwards, however, as Cherry bundled over the line from a maul to give Scotland a one-point lead. Russell added another penalty before Scotland held off France's final charge with a fierce defence.