The primary difference between Louisiana and other states is that Louisiana is a civil law state, whereas all other states in the US are common law states.
This is a very important and interesting distinction, and is a clear reflection of the French history that plays a very prominent part in the development of Louisiana and its legislative and judicial processes.
The primary difference between the two systems is that, under a civil law system, only those things that are explicitly outlined in the statutes of the state are subject to intervention by the judicial branch. If it's not outlined by statute, you can't take someone to court for it.
This is in contrast to the processes used in common law states, where there is a body of law that exists separately from, and in support of, the statutory law. This law is built over time by the holdings and rulings of the judiciary. Claims that are not explicitly outlined in the statutes of the state can still be claimed in court, under the "inherent" powers of equity and law that the courts hold.
Both systems have their benefits and drawbacks; under civil law, the requirements of someone to behave in a legal manner are clear and do not change very often – if it's in the statute, that's what you follow. In contrast, though, new situations that don't clearly fit under existing statutes are a little more difficult to manage under a civil law process.
Common law has the opposite problem, since understanding what's actually allowed or illegal is significantly more difficult, and requires extensive research in case law to know the exact boundaries of acceptable or unacceptable behavior. However, this flexibility allows the courts to expand their authority and acceptable claims without necessarily requiring legislative action.