After dark, a group of men sneaked out into no man's land right up near the German trenches, dragged away the dead horse and replaced it with the model with a sniper inside. He also had a telephone wire that ran back to his own trenches so he could send back reports of German movements.
They kept this up for three days before some German soldier just happened to spot a man climbing out of the dead animal they'd shot a few days before, probably thinking it was giving birth to him, like in that Ace Ventura sequel. Still, they destroyed the decoy, which didn't stop the French from trying it again a few more times.
Some attempts were better than others.