Ireland coach Eddie O'Sullivan is confident O'Driscoll will be ready to take over again for the visit of Wales on Sunday.
'He's had five days of rehab since crying off last Tuesday. He was chomping at the bit, but he just wasn't right.
'I'm very hopeful for next Sunday,' added O'Sullivan. 'It's going to be tight but it's looking good.'
Should O'Driscoll suffer another setback, O'Connell would relish the opportunity to step in again, although he is not convinced he would be the automatic choice.
'I think I was offered it this week to try to change things,' he said. 'To win in Paris takes something different and perhaps that was why I was asked, so I may not be asked to do the job next week.
'I'd love to do it again, but for now, fingers crossed, Brian will return and I can take a back seat again.'
The fact that Ireland held their own for so long was down to a monumental pack performance featuring a devastating attacking maul as their most potent weapon. When Ireland rolled, the French rocked badly - but not often enough to really threaten an upset.
Without O'Driscoll, Geordan Murphy and Denis Hickie were left to provide the fireworks. O'Sullivan's side adopted a narrow approach, although scrum half Peter Stringer excelled on the back foot and Gordon D'Arcy offered some midfield invention.
Ireland benefited from France's laboured efforts to locate third gear. While the back row, Serge Betsen in particular, scaled their usual heights and centre Damien Traille blazed an occasional trail of destruction, the half backs were not convincing. Jean-Baptiste Elissalde's service was shaky and Frederic Michalak's tactical kicking aimless.
Yet France had ample class when it mattered most.
Two Michalak penalties and a Vincent Clerc try dragged the hosts into an 11-3 half-time lead, only for Ireland to hit back in style in the 44th minute. Ronan O'Gara's delicate chip-and-chase ended with the fly half sending Anthony Foley clear down the right to touch down.
O'Gara converted to leave just a point in it, only for the Irish bubble to be promptly burst by two quick tries. Full back Nicolas Brusque's swerving counter-attack from his own half paved the way for debutant lock Pascal Pape to score, before Traille's neat off-load from a tackle sent midfield partner Yannick Jauzion racing in.
Ireland rallied, with D'Arcy wriggling into enough space to tee up wing Tyrone Howe 10 minutes from time. But France had the last word, an Elissalde solo effort bringing try No 4.
Bernard Laporte's side still have plenty to work on, but their veteran flanker Olivier Magne remained in upbeat mood while keeping one eye on the potential Grand Slam decider against England.
'We are very happy because, in the past, our first game was never great,' said Magne. 'I think we played well today, and it's great for our confidence for the rest of the tournament.
'Our target is to raise a level with each game before the England match and I think we have the squad to do it.'
