Jacques Bayard, formerly known as Rene Thibault, is a character in DEXTER. He was a man killed by James Doakes with Angel Batista as the only witness to the shooting, however he didn't see anything but Doakes running after Bayard.
Not much is known about Bayard, aside from his real name being Rene Thibault, and that he was an officer in the Haitian military. But it is assumed that he and Doakes fought against each other on a top secret mission due to the nature of the investigation surrounding his death.
One day while he was walking down the street with groceries he was spotted by Doakes and Doakes yelled at him. At this point Jacques recognized him and began to run and Doakes was in pursuit while Angel was following in the car. After he stopped gunshots were heard and Jacques was dead with Doakes claiming self-defense and that Jacques fired the first shot.
Due to the fishy circumstances, Doakes was under investigation for some time. However, shortly after he informs Lt. Maria LaGuerta that Bayard was a Haitian criminal, specifically a death squad officer, Internal Affairs dropped the case, after being called by an unknown agency in Washington. Apparently the case had to do with "sensitive foreign relation issues". Angel Batista simply states that they "disappeared" the case. Earlier in the episode, after LaGuerta tells Doakes the investigation will be over soon, he responds with "I know it will", implying he knew what would happen.