The Glasgow Warriors back was taken from the field on a stretcher, with Scotland leading 10-7.
Rugby World Cup finalists France clawed back an early 10-0 deficit and responded swiftly to going 17-13 down midway through the second half to triumph, although there were numerous positives for Scotland.
Stuart Hogg and Lee Jones scored their first Test tries, Greig Laidlaw kicked five points and Duncan Weir two, but France responded with tries from Wesley Fofana and Maxime Medard, 10 points from Morgan Parra and a Lionel Beauxis drop goal.
Scottish boss Andy Robinson, who has a contract with the Scottish Rugby Union until after the 2015 World Cup, was asked whether he intends to remain in post or if he might resign at the end of the tournament.
“I can’t hide away from what you’re saying and you’re right to bring it up,” said Robinson of the damning statistics.
“I have total belief that we have the ability to win and that belief was strengthened even more today, as it was against Wales and the England game.”
Robinson lamented the decision of referee Wayne Barnes to award France a second-half penalty, when the head coach believed it should have been given to the hosts for two indiscretions by visiting centre Aurelien Rougerie, who went through a ruck and to ground before kicking the ball while on the floor. The French went on to score a seven-pointer.
However, France head coach Philippe Saint-Andre when questioned about Robinson’s reaction to Medard’s try, wondered about the validity of Jones’ score, which came after John Barclay won the ball cleanly.
“I found the referee very consistent. It was a very quick game with a lot of turnovers by both sides.”
Saint-Andre praised the character of his side and paid tribute to Scotland’s display.
He added: “I’m proud of my team because it was physical, it was hard, but we didn’t panic.
Scotland scorers: Tries: Hogg, Jones. Cons: Laidlaw, Weir. Pens: Laidlaw.
SCOTLAND: Hogg, R. Lamont, S. Lamont, Morrison, Jones, Laidlaw, Blair, Jacobsen, Ford, Cross, Gray, Hamilton, Barclay, Rennie, Denton.
Replacements: De Luca for R. Lamont (31), Weir for Laidlaw (48), Cusiter for Blair (31), S. Lawson for Ford (69), Kalman for Cross (62), Kellock for Hamilton (69), Vernon for Denton (53).
France scorers: Tries: Fofana, Medard. Cons: Pape, Parra. Pens: Parra 2. Drop Goals: Beauxis.
FRANCE: Medard, Clerc, Rougerie, Fofana, Malzieu, Trinh-Duc, Parra, Poux, Szarzewski, Mas, Pape, Maestri, Dusautoir, Harinordoquy, Picamoles.
Replacements: Beauxis for Medard (62), Dupuy for Parra (75), Debaty for Poux (51), Servat for Szarzewski (51), Nallet for Maestri (66), Bonnaire for Picamoles (58).
Referee: Wayne Barnes (RFU).