The result keeps them on course for a Grand Slam showdown with England in Dublin on March 30, although there is the little matter of Wales at the Millennium Stadium before then.
Fly-half David Humphreys, who is rapidly turning the 2003 championship into a personal triumph, celebrated his 50th appearance for his country with a second successive man of the match performance.
The record-breaking fly-half, who led the team out, was unable to unleash the star-studded Irish backline but he ran the show with a superb kicking game and landed four penalties from six attempts. He has now contributed 55 of his side's points this season.
Humphreys' opposite number Francois Gelez scored all France's points with four penalties but he crucially missed another three.
Full-back Geordan Murphy provided the other Irish points with a first-minute drop goal as Ireland made it nine wins in a row and a third victory in four meetings with France, a sure sign of their emergence as a world power.