Both sides experienced difficulty in coping with a swirling wind and persistent drizzle at Lansdowne Road, but Ireland maintained their 100% record thanks to sure-footed fly-half David Humphreys, who kicked four penalties to take his points tally to 55 in three games.
"Because of the weather conditions, France were unable to play their usual expansive game," said O'Driscoll, who has yet to experience defeat as Irish skipper.
"It was our job to make sure they couldn't attack as they usually do and perhaps the weather did play a part in that."
The Irish have now won their last nine matches and have beaten the French three times in their last four meetings to confirm their emergence as a world force.
Although they were unable to add to the eight tries they scored against Scotland and Italy, coach Eddie O'Sullivan was delighted with his side's persistence and patience as they condemned the reigning champions to a second defeat in three games.
"I'm relieved to come out of a tight game," he said "I'm very proud of the team and very happy with the way they stuck to the task.
"It was very important to get a win against a world-class side in very difficult conditions. I think it was a good professional job.
"There were mistakes on both sides. It was probably the ugliest game I've seen for a long time but it's looking a lot prettier when you come out the right side of it.
"That's a good French side who came into the game knowing they could still win the six nations. They really made us work for the victory."