The accident happened near Ruth Bridge Road.
Audie Castille, 51, of St. Martinville died after being struck by the fully marked unit operated by Matthew Alexander, 39, an on- duty deputy.
According to Louisiana State Police, Alexander was traveling northbound on LA 31 when he was unable to avoid striking Castille who was on foot in the northbound lane.
Castille was pronounced dead at the scene. Alexander was not injured.