Russell, 24, was taken off early in the second half of Saturday's Six Nations win at Murrayfield following a collision with Robbie Henshaw.
However, he was cleared to continue after a head injury assessment (HIA), as Duncan Weir returned to the bench.
The influential playmaker has since passed a final assessment.
Russell's former Glasgow Warriors team-mate Weir proved to be a reliable deputy in his seven minutes on the Murrayfield pitch against the Irish, but Scotland head coach Vern Cotter will no doubt be relieved to have such a key player at his disposal for the trip to Paris.
His performances for the Warriors have attracted interest from French Top 14 clubs Toulon and Montpellier in France and from Bath and Gloucester in England.
Russell suffered a concussion during Scotland's 29-18 victory over France at Murrayfield last year, missing the final Six Nations match against Ireland.
He also sustained a severe head injury in Warriors' Pro12 semi-final at the tail end of last season, which ruled him out of Scotland's summer tour to Japan, making his return to action in mid-September.
Media playback is not supported on this device
Scotland fly-half Finn Russell has been cleared to train ahead of Sunday's game against France after recovering from a head knock sustained against Ireland.