Despite the defeat, a try-scoring bonus point means France head the table on points difference from Scotland, with both teams on 16 points. Ireland are still in the mix with 14 points.
Prop Pierre Schoeman and scrum half Ben White also crossed for tries as the Scots ran France ragged with a high-tempo game in the Edinburgh sunshine, and they recorded their highest points tally over France.
The visitors scored tries through wings Louis Bielle-Biarrey and Theo Attissogbe, scrumhalf Antoine Dupont, full back Thomas Ramos (two) and flanker Oscar Jegou, but coach Fabien Galthie will be concerned by their discipline with two yellow cards and how they wilted under pressure.
France have a points difference of +79 and Scotland +21, so it is advantage to the French ahead of their final match at home against England, while Scotland must go to Ireland with both hoping Steve Borthwick's side can spring a surprise.
"The tournament is not over for us yet. We have got ourselves an opportunity next week," Scotland captain Sione Tuipulotu said.
"We have an air-tight change-room. We stuck together after that tough first round (a loss to Italy). We have rallied behind our coach (Gregor Townsend) and I can see the storylines changing.
"Anything is possible now. A lot of people wrote Ireland off too at the start of the tournament, but both of us are still in the championship."
France's Emmanuel Meafou conceded his side were outplayed, but will quickly refocus on the challenge of England.
"The Grand Slam was the goal, but we are still looking to win the competition," he said. "We will take this loss and get back to it next week and take on England.
"Scotland got on top us early in the first half, and then carried that on in the second. We gave ourselves too much of a hill to climb at the end, but credit to Scotland."
Scotland scored four tries in a Six Nations match against France for the first time since their final game of the 1999 Championship, when they last won the title, something they hope will be an omen for this year.
Late rally from France
It was only a late burst from the visitors as they scored three tries in the final six minutes that narrowed the scoreline at Murrayfield and denied Scotland a record winning margin.
Graham bagged a Scottish record 36th international try to open the scoring inside five minutes, before France went into a 14-7 lead as Bielle-Biarrey scored one try and created the other for Attissogbe.
But from there, Scotland turned the screw, winning the collisions and playing at a pace that France found unable to contain as the home side scored 40 unanswered points to seize control of the contest.