The Scots, led by 50-cap winning skipper Jason White, believed they could shock the traditionally slow starters especially after giving them a scare on the opening day of the last campaign in Paris.
They sent out an early warning to the pre-tournament favourites early on but White spilled the ball from a crunching tackle and Simon Taylor knocked the ball on, just short of the line.
But last season's runners-up did not heed those signs and Scotland forced themselves ahead with their first try in the 11th minute with Blair spreading play and Lamont crashing over the line.
Chris Paterson converted before his trusty right-foot sent over a 22nd-minute penalty from 35 metres after the French had been penalised for having their hands on the deck.
The talented Edinburgh wing then made it 13-0 with another penalty after he had been taken out illegally by Cedric Heymans following another great piece of work from the impressive Blair.
Jean-Baptiste Elissalde gave the visitors some hope to take into the dressing room at the break by reducing the scoreline to 10 points with a penalty.
But it quickly became a state of emergency for the French just seven minutes after the interval.
The Scottish pack pushed their opponents back to towards the
try line and Lamont forced the ball down for another score which Paterson again converted.
But that sparked an angry French riposte with Julien Bonnaire going over in the corner but Elissalde eased the pressure on the home nation as his kick, from tight to the touchline, hit
Blair was forced off in the 56th minute with a bleeding nose and the introduction of Cusiter coincided with a change of luck for Scotland with Paterson missing the easiest of his kicks.
Elissalde punished his rare slip moments later by sending a long-range penalty through the posts to set up an anxious finale.
Sebastien Bruno added to the tension inside Murrayfield by forcing the ball over the line in the corner, with three minutes remaining, but Elissalde pulled his kick wide to bring a united sigh of relief.