Nimes's victory lifted them a spot up to 18th, on 29 points.
Lille, who have won only two of their last six league games, were caught off guard early as Kone curled a superb shot into the top corner to put the visitors ahead on 12 minutes.
It did not take Lille long to react.
In the 20th minute, Xena equalised with a downward header from Jonathan Bamba's corner.
Lille had two goals, by Burak Yilmaz and Xeka, disallowed as they pushed for a late leveller.