Jacques Bayard - Formerly a death squad officer named Rene Thibault working for the Haitian government and at one point came to blows with James Doakes. He left and went to start anew in Miami when he was spotted by James Doakes and ended up being shot and killed by him.
Detective (then) Angel Batista - In the car with Doakes when he spotted Bayard and drove the car in pursuit of him. Heard Doakes gun go off first and then Bayard's, reported this to IA.
Sergeant-Detective James Doakes - In the passenger side of the car when he spotted the war criminal and told Bayard to stop. He pursued him and shot and killed him. Attempted to lie about who shot first and where he fired from but all was revealed by Dexter's blood work and Angel's testimony.
History Leading up to the Shooting
While Doakes was in the special forces unit of the army he was sent to Haiti were he saw death squad officers killing thousands of people and Jacques Bayard was one of these death squad officers. Bayard eventually retired from that life and decided to form a new one in Miami. When James was riding shotgun in Batista's car he recognized him and pursued him. James then took out his gun and shoot Bayard before he could get a shot off, effectively killing him. But not before a death impulse triggered his finger to pull off one shot at the column under the bridge.
Jacques Bayard - Shot dead by Doakes when he recognized him and pulled out a revolver trying to defend himself.
Fallout from Shooting
After the shooting, Sergeant Doakes was put on suspension pending a full investigation. Ultimately the case was closed when LaGuerta called an unknown Washington agency and got them to drop the case due to international security risks. Angel was temporarily treated as a snitch by the rest of the department but Doakes, knowing Angel is a good cop, made an officer apologize to Angel in front of the whole department making it clear he didn't want Batista to pay for something he knows he did.
Fate of Shooters(s)
Bayard was killed in the ensuing gunfight by James Doakes and his death was covered up even though there was evidence to suggest that it was a premeditated murder.