O'Driscoll sustained the injury last month and has been ruled out of the trip to Paris as coach Eddie O'Sullivan admitted defeat in his battle to include his new skipper - who only replaced Keith Wood after the World Cup.
O'Sullivan said: "Brian was very close, Saturday just came a little bit too soon. If it was a Grand Slam decider then we might have played him, but it's the first match so there's no point taking risks.
"Paul O'Connell is an excellent choice as skipper - he was one of the outstanding players of the World Cup and he has the respect of all the players. He has everything you want in a skipper."
Leinster centre Gordon D'Arcy has been given the task of filling O'Driscoll's boots in what will be his first start for the national side - he has already accumulated five caps as a replacement.
He will partner Kevin Maggs in midfield with Munster's Ronan O'Gara getting the nod over David Humphreys at fly-half, although the Ulster number 10 features among the replacements.
Malcolm O'Kelly will join O'Connell in the second row for his 60th cap - he becomes the fifth Irishman to reach that milestone - forcing Donncha O'Callaghan to settle for a place on the bench.
Simon Easterby, Keith Gleeson and Anthony Foley make up the back row with Victor Costello included as back-up.
Ireland team to face France in the RBS 6 Nations, Paris, February 14: G Dempsey; S Horgan, G Darcy, K Maggs, T Howe; R O'Gara, P Stringer; R Corrigan, S Byrne, J Hayes, M O'Kelly, P O'Connell (captain), S Easterby, K Gleeson, A Foley.
Replacements: F Sheehan, S Best, D O'Callaghan, V Costello, G Easterby, D Humphreys, A Horgan.