The home side led 13-3 at the break thanks to a Vincent Clerc try and two Dimitri Yachvili penalties but Ireland fought back early in the second period.
Triple Lions tourist Ronan O'Gara slotted a hat-trick of second-half penalties to bring Ireland to within a point before Yachvili added two more of his own in the final 15 minutes to seal the win.
Ireland had two chances to snatch a draw late on but they surrendered a five-metre scrum and a close-range lineout as France held on.
Ireland will hope to reverse the result when the two sides meet again in Dublin next Saturday, two days before the deadline for World Cup squad announcements.
And having insisted that game time would be key ahead of this World Cup giving the failings following a limited build up in 2007, Kidney will be desperate for a victory at the Aviva Stadium.
The former Munster boss will hope to welcome back Lions legend Brian O'Driscoll who is yet to fully recovered from a neck and shoulder injury but fellow Lions Stephen Ferris and Gordon D'Arcy remain major doubts.
Kidney is expected to hand 2009 Lions captain Paul O'Connell and Lions Test stars Jamie Heaslip and David Wallace a start after O'Connell came off the bench, Heaslip was an unused replacement and Wallace was rested altogether in Bordeaux.
After welcoming France to their new home next weekend, Ireland conclude their warm-up matches with a home tie against England prior to their opening World Cup clash with the United States on September 11.