O'Driscoll (hamstring) and Stringer (hand) sustained their injuries in last weekend's 19-9 defeat of Wales and despite treatment, will both miss Ireland's second match of the championship.
The Irish back line for the French game has been reshuffled due to the withdrawals - Shane Horgan moves into the centre to partner Gordon D'Arcy, while Geordan Murphy comes onto the right wing in place of Horgan, with Andrew Trimble confirmed on the replacements bench.
With Stringer absent at scrum half, Isaac Boss will make his first RBS 6 Nations championship start in his place, with Eoin Reddan his back-up on the bench.
O'Sullivan also confirmed that number 8 Denis Leamy came through training, so Jamie Heaslip is not considered for the replacements.
The Ireland team will be captained by Munster lock Paul O'Connell.
IRELAND TEAM AND REPLACEMENTS (v France, Croke Park, Sunday, February 11, kick-off 3pm):
15 - Girvan Dempsey (Terenure College/Leinster) 70 caps
14 - Geordan Murphy (Leicester Tigers) 44
13 - Gordon D'Arcy (Lansdowne/Leinster) 27
12 - Shane Horgan (Lansdowne/Leinster) 51
11 - Denis Hickie (St. Mary's College/Leinster) 54
10 - Ronan O'Gara (Cork Constitution/Munster) 67
9 - Isaac Boss (Ballymena/Ulster) 5
1 - Marcus Horan (Shannon/Munster) 43
2 - Rory Best (Belfast Harlequins/Ulster) 8
3 - John Hayes (Bruff/Munster) 69
4 - Donncha O'Callaghan (Cork Constitution/Munster) 3
5 - Paul O'Connell (Young Munster/Munster) 40 (capt)
6 - Simon Easterby (Llanelli Scarlets) 53
7 - David Wallace (Garryowen/Munster) 33
8 - Denis Leamy (Cork Constitution/Munster) 18
16 - Jerry Flannery (Shannon/Munster) 10
17 - Simon Best (Belfast Harlequins/Ulster) 13
18 - Mick O'Driscoll (Cork Constitution/Munster) 5
19 - Neil Best (Belfast Harlequins/Ulster) 7
20 - Eoin Reddan (London Wasps) 1
21 - Paddy Wallace (Ballymena/Ulster) 2
22 - Andrew Trimble (Ballymena/Ulster) 11