Benjamin Andre had given the home side the lead early on, but Vincent Nogueira found an equaliser with practically the last kick of the game to rescue a point for Sochaux at Stade Francois Coty in a tight game that mainly lacked quality in the final third.
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The hosts got off to a flying start and went ahead in the eighth minute. Mehdi Mostefa's run down the right flank ended with a pass across the face of goal, which found its way to the back post where Andre was lurking to scuff the ball home.
However, Sochaux scored an equaliser in stoppage time at the end of the match when Nogueira found himself free at the back post from a corner before heading in the leveller.
The draw leaves Ajaccio bottom and Sochaux in 19th place on 10 and 12 points respectively as they both face the prospect of relegation from the French top flight.