The margin levels of French food retailers are debated at every farm crisis. The main objective of this article is to statistically identify the eventual existence of market powers of these retailers. In order to overcome missing data on their distribution costs, we develop an original framework of the French system of temporary limits on margins in case of a market crisis. Our econometric results conducted on two fruit and vegetable products indicate that this system is effective with significant reductions of these margins during market crises. Above all, our statistical results indicate that the French food retailers simultaneously modify their margins on other products, attesting the presence of market powers to the detriment of the organic sectors.