Is there a self defense law in Louisiana?

Yes, depending on the circumstances, of course. Mississippi has adopted what is generally called a "Castle Doctorine" or "Stand Your Ground" law. This gives citizens who feel that their lives are in immediate danger the right to "stand their ground". This applies to one's home or "Castle" (and in MS, one's private property-though one's vehicle is included, the circumstances under which deadly force is acceptable are debated). The issue is not nearly this cut and dry, for more info look at:

§ 97-3-15. Homicide; justifiable homicide; use of defensive force; duty to retreat. (3) A person who uses defensive force shall be presumed to have reasonably feared imminent death or great bodily harm, or the commission of a felony upon him or another or upon his dwelling, or against a vehicle which he was occupying, or against his business or place of employment or the immediate premises of such business or place of employment, if the person against whom the defensive force was used, was in the process of unlawfully and forcibly entering, or had unlawfully and forcibly entered, a dwelling, occupied vehicle, business, place of employment or the immediate premises thereof or if that person had unlawfully removed or was attempting to unlawfully remove another against the other person's will from that dwelling, occupied vehicle, business, place of employment or the immediate premises thereof and the person who used defensive force knew or had reason to believe that the forcible entry or unlawful and forcible act was occurring or had occurred. This presumption shall not apply if the person against whom defensive force was used has a right to be in or is a lawful resident or owner of the dwelling, vehicle, business, place of employment or the immediate premises thereof or is the lawful resident or owner of the dwelling, vehicle, business, place of employment or the immediate premises thereof or if the person who uses defensive force is engaged in unlawful activity or if the person is a law enforcement officer engaged in the performance of his official duties;

(4) A person who is not the initial aggressor and is not engaged in unlawful activity shall have no duty to retreat before using deadly force under subsection (1) (e) or (f) of this section if the person is in a place where the person has a right to be, and no finder of fact shall be permitted to consider the person's failure to retreat as evidence that the person's use of force was unnecessary, excessive or unreasonable.