Griezmann volleyed home eight minutes into stoppage time but the goal was ruled out as the forward was offside when Aurelien Tchouameni sent the ball into the area
The ball was deflected by a Tunisian defender into the path of Griezmann, who was onside at that point, but the effort was disallowed and Tunisia won the game 1-0.
"We are writing a complaint after Antoine Griezmann's goal was, in our opinion, wrongly disallowed. This complaint has to be filed within 24 hours after the final whistle," the FFF said in a statement.
Tunisia were eliminated from the tournament while France advanced top of Group D into the last 16 and they will face Poland on Sunday.
The FFF did not specify whether the complaint was over the goal itself or the fact it was ruled out after the final whistle.