A family member reported through social media that Delaune passed away about 1 p.m. Monday.
Delaune, 28, was traveling east on La. 182 at 10:20 p.m. Saturday, when he ran off the right side of the road and entered the south ditch.
His vehicle struck two culverts before overturning, according to State Police Troop I Public Information Officer Stephen Hammons.
Delaune was the only occupant of the vehicle. He was not wearing a seatbelt and was ejected, sustaining critical injuries, Hammons said.
In an unrelated incident, a father was killed while walking along the U.S. 90 frontage road near Centerville with his two young children.
Lester Redeaux, 40, of Centerville was struck by a 2003 Chevrolet Impala driven by Aaron Burgess, 39, of Franklin.
Seth Redeaux, 2, of New Iberia also was struck and received moderate injuries. Kedra Redeaux, 11, of Centerville was not hit.
The three pedestrians were walking east in the roadway, with the traffic, on the frontage road near La. 318. The Impala was eastbound on the same road approaching the pedestrians from behind when they were struck. The driver returned to find the two children in the roadway. He searched the area and found the father in the ditch between the frontage road and the highway, Hammons said.
S. Redeaux was treated for moderate injuries at Franklin Foundation Hospital and released. The father was transported to Our Lady of Lourdes Regional Medical Center in Lafayette by AirMed where he was pronounced dead, Hammons said.
K. Redeaux was not injured, nor was the driver of the Impala.
Routine toxicology samples have been obtained and submitted to the Louisiana State Police Crime Lab for analysis. This crash remains under investigation, Hammons said.
Louisiana state law requires that all pedestrians walk on the far left side of the roadway against the flow of traffic. Pedestrians also are required to walk on the sidewalk if one is provided.
Alcohol is not suspected to be a factor in this crash, according to police.
Elsewhere, a traffic snarl between 4-6 p.m. along U.S. 90 near Patterson was the result of an 18-wheeler which broke down.
Sheriff Mark Hebert said the traffic was routed onto La. 182 via Red Cypress Road.