Sue: It's likely an article did appear in "The Advocate" but could also have appeared in other papers such as one in Lafayette or Opelousas, it might depend on exactly where the accident occurred. Since the injured were taken to BR, it's likely that the accident occurred near there. However, you lack enough precise information to effectively search (exact date, location, name of deceased, etc.). Am I to assume that none of the injured are still living? Otherwise, I would think that anyone who survived such a tragedy would certainly remember at least some of the details. In any event, microfilm copies of the "Advocate" for the period are held by around 16 libraries but they are all in Louisiana with the exception of the Library of Congress (DC). Yet searching for one or two articles within a 3 year period in a fairly large daily paper is quite a job and could take many, many hours.
The only other thing I can suggest is to contact the LA State Police, Traffic Records Unit at 225-925-6156 just to see if they archive "crash reports" this far back. You might want to specify that it was with a fatality since they might not archive every little fender-bender. Again though, without more details they might not be able or willing to pull such a report IF it even survives. You just don't know until you ask.