"I'm trying all the tactical options," said McGeechan. "Greg remains an important element for the team but I wanted to try him at centre.
"Some of these changes are purely tactical. We looked at what happened against Ireland and tried to make some changes in midfield."
The other significant change is the introduction of Brenden Laney at fly-half as replacement for Leeds' Gordon Ross, who had a difficult afternoon against the Irish.
"Last week we got only six points - not good at all for us," added McGeechan.
"We had opportunities but didn't seize them. Against France we must keep the scoreboard moving."
Scotland team to play France in Paris:
Backs: G Metcalfe (Glasgow); C Paterson (Edinburgh), G Townsend (Borders), K Utterson (Borders), K Logan (Wasps); B Laney (Edinburgh), B Redpath (Sale Sharks, capt).
Forwards: T Smith (Northampton), G Bulloch (Glasgow), B Douglas (Borders), S Murray (Edinburgh), S Grimes (Newcastle), M Leslie (Edinburgh), S Taylor (Edinburgh), A Mower (Newcastle).
Replacements: S Scott (Borders), G Kerr (Leeds), J White (Glasgow), J Petrie (Glasgow), M Blair (Edinburgh), G Ross (Leeds), A Craig (Orrell).