Leinster full-back Dempsey was a late withdrawal from the Irish team to play Italy after failing to recover in time from a groin strain. His place was taken by Geordan Murphy, who turned in an impressive performance against the Italians.
Leicester star Murphy had replaced Horgan early in the first match against Scotland at Murrayfield on February 16 when the winger suffered a hamstring injury while O'Gara has not played since Munster's Celtic League final victory over Neath in Cardiff on February 1, when he was stamped on the ankle by flanker Brett Sinkinson.
Harlequins fly-half Burke is the player to make way for O'Gara in the Ireland squad and has rejoined the A squad.
Ireland squad for the RBS 6 Nations clash against France:
Forwards: S Byrne, V Costello, L Cullen, J Fitzpatrick, A Foley, Keith Gleeson, J Hayes, M Horan, G Longwell, M O'Kelly, Alan Quinlan, F Sheahan.
Backs: G Dempsey, G Easterby, R Henderson, D Hickie, S Horgan, D Humphreys, J Kelly, K Maggs, G Murphy, R O'Gara, B O'Driscoll (capt), P Stringer.