The French system of laws is a civil law system that is based upon the Napoleonic Code, and further back the Justinian Code. The legal system in Louisiana is now bijuridicial retaining some of the elements of the Napoleonic Code.
But, why did the rest of the land that was purchased as part of the Louisiana Purchase not adopt a civil law system, like Louisiana did? All of the other states that were originally part of the Louisiana Purchase now have common law systems.