The Main Question
when a court case is decided in Louisiana, can it establish precedent
in other states that follow common law?
The court decisions of a sister state are always persuasive authority. This applies even to trial court rulings and rulings from other countries that are not precedents in any U.S. state. Similarly, courts can look to legal treatises and sources like the Restatements of Law that have not been adopted or approved by any public official as persuasive authority. In theory, it would not even be improper for a state court judge in say, Texas, to quote from a Mock Court Brief of a high school student as persuasive authority.
This is because the value of a persuasive authority (as opposed to in state binding authority of an appellate court) in states that follow common law, is that the reasoning of the ruling is intrinsically informative and is reliable because it comes from someone learned in the relevant law and familiar with the legal issues in question.
Someone could reasonable dispute persuasive authority from Louisiana on the ground that the substantive law rule in Louisiana expressed in its statutes and prior case law, which a Louisiana court is interpreting, is different from the law in the state where the Louisiana court decision is utilized.
For example, suppose that Louisiana has not statutorily adopted the equitable doctrine of laches which is a case law doctrine derived from English courts of equity which denies relief to people who make claims who have slept on their rights without taking legal action in a manner prejudicial to the defendant, even if no statutory statute of limitations applies. If a case allowing relief within the statute of limitations in Louisiana where facts justifying the application of the doctrine of laches were present in an Ohio case, it would be fair to argue that the Louisiana precedent should not be followed as persuasive authority, because Louisiana is a state that has not adopted the doctrine of laches, while Ohio is a state that has adopted the doctrine of laches.
But really, this means of distinguishing a Louisiana precedent is no different from the way that a precedent from any other state would be distinguished. Louisiana court precedents are not less persuasive on the theory that a court precedent in Louisiana's court system doesn't have the same effect as a court precedent in states with purely common law legal systems.
Furthermore, as explained below, while civil law systems in other countries do not afford the same status to appellate court decisions that common law jurisdictions do, Louisiana, in this regard, is closer to the common law system than it is to the civil law system, in any case.
Louisiana Law Is A Complex Civil Law And Common Law Hybrid
In practice, Louisiana law is more of a hybrid system, than it is a true civil law state (as it is often described as being). The Louisiana Purchase of 1803 actually preceded the adoption of the French Civil Code in 1804, although the French Civil Code had profound influence on Louisiana law prior to it becoming a U.S. state in 1812, and its early years of U.S. statehood when the federal governments role in law making and providing government services was much narrower.
I. Sources Of Law
Consistent with its civil law heritage, all law in Louisiana must be rooted in statute and can't be purely dependent upon common law case law.
But, Its courts, unlike true civil law states, issue appellate decisions that are binding precedents in common law fashion.
Unlike true civil law systems, precedent making case law from appellate courts regarding statutory interpretation is essentially the same in Louisiana as in other U.S. states with a common law heritage.
Where the statutes of Louisiana provide a hook for legal rights that aren't fully explained, for example, in tort law, Louisiana courts even sometimes look to the Restatements of the Law which purport to set forth in code-like fashion the common law applicable in other states, to guide the gap filling roles of courts in applying its private law statutes.
II. Civil Procedure
Civil procedure in Louisiana is a mix of the civil legal process and the common law legal process. In civil procedure, Louisiana has some civil law influences, but is a common law civil procedure biased hybrid system.
While it is not compelled by the U.S. Constitution, Louisiana has a right to jury trials in many civil law case.
Louisiana's overall civil law system is better characterized as a whole as adversarial than inquisitorial, despite residual civil law influences.
III. The Legal Profession
The ethical duties of lawyers in Louisiana, likewise, now fully track those of lawyers in other U.S. states. Louisiana has almost completely abandoned any trace of the occupational framework for lawyers and the ethical standards for lawyers found in civil law countries that differ from those of U.S. common law jurisdictions.
For example, Louisiana does not have the ethical rule for lawyers found in most civil law jurisdictions forbidding lawyers from representing someone in a matter in which a previous law has done work for which the previous lawyer has not be paid. Likewise, Louisiana does not have the strict regulation of lawyer contact with witnesses prior to their presentation of testimony to a court that is found in most civil law jurisdictions but is absent in U.S. common law jurisdictions.
Similarly, notaries in Louisiana were originally closer to the civil law model but the role of notaries has eroded in the common law notary direction over time (not necessarily completely however).
IV. Private Law
The substantive private civil law in Louisiana (i.e. the non-criminal law that can be raised in lawsuits between non-governmental parties such as contract law, tort law, property law, inheritance rights, marital property, guardianship, customary units for real property boundaries, etc.) tends to track the French Civil Code adopted a year after the Louisiana purchase (and the pre-French Civil Code law that applied during French rule), rather than English common law.
For example, usufructs exist in Louisiana law but are unknown in common law jurisdictions.
Bit by bit, distinctive Louisiana legal concepts such as the "mystic will" have been repealed or fallen into desuetude, however.
Until about the 1840s, Louisiana's laws governing slavery and interracial relationships followed the customs and practices established under French rule which were quite different from the practices of the English adopted in the colonial period in the United States. But in the decade or two before slavery was abolished in Louisiana this began to shift markedly in the direction of other southern and for a while Confederate, states in the United States and away from the French model, curtailing greatly, for example, the rights of "free people of color" in the state.
This said, however, many provisions of private law that are present in other U.S. states have been adopted wholesale in Louisiana.
For example, Louisiana has adopted the Uniform Commercial Code, the Uniform Fraudulent Transfers Act, the Uniform Child Custody Jurisdiction Act, and
"no fault" divorce.
Many parts of private law, such as the law of union-management relationships and arbitration are governed by federal law in a common law mold.
Louisiana has also, in civil law fashion, statutorily codified legal concepts not present in civil law countries like trust law in order to coordinate functionally with trust law in other U.S. states.
Likewise, there are many major modern legislative developments in civil law countries generally, and French law, in particular, were not imitated by Louisiana.
For example, France has adopted innovated ways to recognize relationships short of marriage that Louisiana has not copied, such as civil solidarity pacts (PACS) and some minimal legal rights associated with cohabitation known in French as a concubine relationship status.
V. Criminal Law
Criminal law in Louisiana is much closer to the common law adversarial system than the civil law inquisitorial system, for example, in part as a consequence of U.S. Constitutional limitations on state criminal procedure.
VI. Public Law
Public law in Louisiana (i.e. the law governing the relationship of individuals with the government) almost entirely tracks the common law pattern and not the civil law pattern, in part, due to the influence of U.S. Constitutional law and federal statutes (e.g. 42 U.S.C. § 1983).
Footnote On Puerto Rico A Hybrid That Is Primarily A Civil Law System
Puerto Rico became in U.S. territory in 1898 in connection with the Spanish-American War, at a time when its civil law institutions were much more developed than those of Louisiana in 1803, has remained Spanish speaking while still subject to U.S. federal law, and is not as integrated into the U.S. legal system as Louisiana and other U.S. states in its current Commonwealth status (which may face another referendum on its status soon under a bipartisan bill passed by the U.S. House on December 15, 2022).
As a result, while Puerto Rico must make some concessions to the U.S. Constitution which incorporates common law legal institutions like the right to a jury trial in criminal cases, it is much closer to the European (and in particular, the Spanish) civil law legal system than Louisiana.
However, importantly, federal courts in Louisiana operate using the common law based federal rules of procedure, criminal and civil, and apply common law based substantive federal law.
Note On Sources
This answer is based predominantly on snippets here and there of encounters with Louisiana law, reviews of surveys of state laws in various areas, history books, historical fiction that is well researched with respect to law, new accounts, and other similar sources gathered piecemeal from memory.
I'm not an expert in this area and there may be minor inaccuracies that I will correct if I learn of them, but in the land of the blind, the one eye'd man is king, so I'm offering insight into the subject greater than the vast majority of educated lay people and even the vast majority of U.S. lawyers outside Louisiana.