If child gets into a car accident with car in parent's name is the parent liable

Please note that I am licensed in New York and this is for general information purposes only.

Although I am not sure about the specifics of auto insurance law in Louisiana, I can tell you that in New York, you would be liable for vicarious liability/negligent entrustment of the vehicle to your son. The injured person may be able to sue your son as well as you, individually. Assuming your son is a legal adult, the best preventative measure is for him to purchase a vehicle in his own name and take his own insurance out.

This answer is for educational purposes only.

I am a Maryland lawyer so you should verify that the law is the same in your state. Ordinarily a parent is not liable for a child's car accident. One common exception is for negligent entrustment. If a child has had several car accidents, serious tickets etc. such that the parent knew or should have known that the child was unsafe to drive then the parent could be liable for entrusting a car to the child.

An even harder legal theory in the parent-child setting is to establish that the child was acting as the parent's agent at the time of the accident.

With a teenage child the best way to deal with minimizing your risk is to speak to a good insurance agent. If your child is involved in a very serious accident most lawyers will explore any and all legal theories to hold the parents liable if there is not enough insurance.