He was a war criminal killed by James Doakes.
Not much is known about Bayard, aside from his real name being Rene Thibault, and that he was an officer in the Haitian military. He and Doakes fought against each other during a top secret mission.
One day, while Bayard was walking down the street with groceries, he was spotted by Doakes who yelled at him. Bayard recognized him and began to run, with Doakes in pursuit and Angel following in the car. Angel heard gunshots and Jacques was found dead with Doakes claiming self-defense and saying that Bayard had fired the first shot.
Due to the fishy circumstances, Doakes was put under investigation. Lt. Maria LaGuerta asked Doakes about the shooting and he said that Bayard was a Haitian criminal, specifically a death squad officer.
Eventually, 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." This astounded Angel Batista and he stated that they "disappeared" the case. Earlier in the episode, LaGuerta told Doakes the investigation would soon be over soon, and he responded with, "I know it will." This implied that he knew the government would protect him..