Kearney left proceedings at Stade de France just before half-time after suffering damage to his right knee medial ligament.
Ireland head to Twickenham on Saturday, 27 February having lost their 12 match unbeaten run which dated back to November 2008. It was also the first championship defeat suffered by Declan Kidney since taking over as Irish coach.
France were 17-3 ahead at half-time and 10 of those points came when Leinster prop Cian Healy was in the sin bin for an early tackle on Francois Trinh-Duc. The home side ran in three tries and the only meaningful response from Brian O'Driscoll's men came in the shape of a try from back row man David Wallace.