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"Rory is under the care of the orthopaedic surgeons at Edinburgh Royal Infirmary. He was undergoing surgery this lunchtime to stabilise a fracture to his fibula," Scotland team doctor James Robson said in a Scottish Rugby statement.
Lamont suffered the injury while contesting a kick half an hour into the contest which France won 23-17 to leave Scotland with three defeats from three and facing a battle to avoid finishing bottom of the standings.
Scotland suffered other injury woes in the game, with scrumhalf Mike Blair hobbling off with a dead leg.
Flyhalf Greig Laidlaw "appeared" to have suffered a concussion, the statement added while centre Sean Lamont sustained an abrasion to his right eye and fellow back Graeme Morrison will require further assessment for a knee injury.
Scotland next play Ireland in Dublin on Saturday March 10.