Despite conceding two first half tries Morgan Parra kept Les Bleus in the game with his kicking before Maxime Médard scored France's only try midway through the second half.
And though Jamie Heaslip scored a third Irish try with ten minutes remaining, France were able to hold out for a fortunate victory.
"We gave ourselves a chance at the end to win it and we didn't take it," said former British and Irish Lions captain O'Driscoll.
"We probably looked the more threatening side but we would prefer to win ugly.
"It was a lot better than last week though. We're definitely going in the right direction.
"We spoke during the week that we couldn't afford to give away needless penalties because they will keep the scoreboard ticking over but that's what happened.
"We are hurting ourselves with a bit of indiscipline and careless turnovers at crucial times.
"They had the lion's share of possession but every time we got to the green zone, I felt we would score tries."