Despite Saturday's defeat, a try-scoring bonus-point means France head the table on points-difference from Scotland with both teams on 16 points from their four games. Ireland are still in the mix with 14 points.
Prop Pierre Schoeman and scrumhalf Ben White also crossed for tries as the Scots ran their illustrious visitors ragged with a high-tempo game in the Edinburgh sunshine, ultimately recording their highest points tally over France.
The visitors scored through Louis Bielle-Biarrey -- who made it nine Six Nations matches in a row in which he's gone over the try line -- Theo Attissogbe, Antoine Dupont, Thomas Ramos (two) and flanker Oscar Jegou.
But coach Fabien Galthie will be concerned by their discipline with two yellow cards and won't be happy about the manner in which they wilted under pressure.
France have a points-difference of +79 and Scotland +21, so it is advantage France ahead of their final match at home against England, while Scotland must go to Ireland with both teams 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's Australian captain Sione Tuipulotu said.
"We have an air-tight change-room. We stuck together after that tough first round defeat 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 they'll quickly refocus on the challenge of England.
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.
It was only a late burst from the visitors that narrowed the scoreline at Murrayfield and denied Scotland a record winning margin.
Graham scored 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.
