If he's now running away, I don't see how you could justify deadly force. Deadly force is generally authorized in Louisiana when someone is breaking into your car and YOU are in it, when someone is breaking into your house and you are in it, or when someone is personally attacking you and that is the force required to protect yourself.
In this case, if you chased this guy down with your car after he started running and killed him, you would be liable because you became the aggressor.
The answer given here should be considered general and should not be considered legal advice, or that there has been an attorney-client relationship established. It is always suggested to retain the counsel of a lawyer for legal advice specific to your situation.