The Irish made a winning start to the championship with a 19-9 triumph over Wales in Cardiff on Sunday but failed to live up to the expectations raised by a remarkable autumn series.
Victory owed as much to Wales' lack of a cutting edge that could turn possession and territory into points as Ireland's own efforts to negotiate a tricky first hurdle.
They won the try count 3-0 with Rory Best, Brian O'Driscoll and Ronan O'Gara crossing but there was a feeling they had made a lucky escape at the Millennium stadium.
France thrashed Italy 39-3 in the tournament opener and O'Sullivan knows the defending champions will be less forgiving than Wales if his side are in a generous mood.
"The areas we need to tighten up on are our discipline and control of the ball," he said.
"If we play loose against France we'll have a problem because they're as good as anybody at running the ball back.
"The French are a different proposition to the autumn when they struggled and they'll be happy with their result in Rome as they controlled the game.
"France were slow out of the blocks and Italy should have had six points on the board.
"But suddenly Italy were 6-0 down after conceding a turnover and that knocked the stuffing out of them.
"They will be disappointed by the way they fell away at the end but France are like that - if you give them that confidence and go forward, then they can take it away from you.
"It's the same for us next week - if we let France play the way they want to then it will be very difficult.
"We'll have a different gameplan for France. If we are not more accurate in aspects of our game we'll create an environment for France to run things."
Ireland's last visit to Cardiff saw them crack in the face of a fierce Welsh onslaught but yesterday they showed greater resilience than two years ago.
The opposition were weaker this time - Wales were missing gamebreakers such Gareth Thomas, Tom Shanklin and Shane Williams - but O'Sullivan insists their survival was down to composure.
"We didn't hit the ground running in the Six Nations because we weren't as accurate as we wanted to be," he said.