The Scotland captain came off after 25 minutes in Paris and was later seen with crutches and wearing a protective "moon boot".
Laidlaw will see a specialist later this week to determine the best treatment option and also how long he is likely to spend on the sidelines.
He was replaced by Ali Price, the 23-year-old winning just his second cap, while Finn Russell took over the kicking duties.
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Both committed serious errors – Price giving away a needless penalty for shoving a French player and Russell missing a simple conversion from in front of the posts – to reinforce the importance of Laidlaw to the team.
But they will have to play their remaining three Six Nations fixtures without him after a scan at his club side Gloucester revealed ligament damage in his ankle.
Greig Laidlaw has been a crucial player for Scotland since becoming captain in 2011
The scrum-half has 58 caps to his name and had been expected to pass the 600-point mark during the championship as Scotland's main goal-kicker.
Coach Vern Cotter is expected to call up Edinburgh's Sam Hidalgo-Clyne to compete with Price for the No 9 shirt when the Scots resume their Six Nations campaign against Wales at Murrayfield on February 25.
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Greig Laidlaw cut a disconsolate figure after playing less than half an hour before getting injured
Cotter has targetted two wins the 2017 edition of the competition and already has one after Scotland beat Ireland on the opening weekend 27-22.
But Laidlaw's injury is one of a number of players who became collateral damage during the bruising 22-16 defeat to France.
Flanker John Barclay took over the armband when Laidlaw limped off against Les Bleus, but was soon himself replaced after suffering a head knock.
Jonny Gray became the Scots' third skipper of the day when Barclay was replaced and could lead the side against Wales.