Louisiana comprises, more or less, OTL US states of Louisiana, Arkansas, Missouri, Iowa, South Dakota, Nebraska, Kansas, Oklahoma, Montana, Wyoming, east Colorado, east and north Texas and south Minnesota.
In 1763, the French territory of Louisiana was ceded to Spain, which developed a slow process of exploration and colonization, mostly limited to New Orleans and surrounding areas.
After the independence of the English colonies, some Anglo settlers moved to upper Louisiana, but the number was still small in 1800.
In 1822, Louisiana declared independence from Spain and the new government claimed all territories between the Mississippi and the Colorado River (OTL Colorado, Texas), with no very defined borders in the north and northwest. The independence war lasted three years in which Louisiana got some support from Georgia and Virginia, and joined the independentist movement in Monterrey and Mexico.
Louisiana tried to assimilate Anglo settlers west of the Mississippi as Louisianan citizens, but did not promote further immigration. This lead to some conflicts against Virginian and Georgian settlers. Another permanent conflict was with the Indians. According to Louisianan constitution, Indians were equal citizens, but white settlers, specially Anglos, found this problematic, and Louisianans, themselves, did not agree with own national status for the Indian tribes.
In 1834, an incident provoked the declaration of war by Virginia. There were some clear indications that Virginia pretended to annex most of Louisiana Territory. Columbia, who was also worried by Virginian expansion and the possibilities that they would deny transit on the Mississippi joined the war against Virginia. Monterrey and Mexico also supported Louisiana, plus most Indian nations.
The war ended in 1837, which most fighting occurring in Virginian soil by Columbian army.
A bi-national commission was set in 1839 to explore and mark the limits between Louisiana and Columbia. The expedition finished in 1842 and both nations confirmed the limits at the Mississippi and the 46th parallel.
Less successful was a commission to settle the borders between Louisiana and Monterrey, which developed into a shooting war in 1843. Mediation by Mexico, the United Kingdom and Columbia put end to this conflict. Also, a "continental divide" unspecified at this time would mark the western limits of Louisiana to both California and British Oregon.
The definitive borders were finally settled in 1894.
Given the importance of plantations in earlier Louisianan economy, slavery was preserved after independence. This was in conflict with several liberal thinkers, who managed to ban slavery north of Arkansas River in 1833 (one of the causes of the war against Virginia).
In 1837, Louisiana forbid importation or exportation of slaves, or re-enslavement of any free citizen, and in 1850 a law passed declaring every child born from January 1st, 1851, to be free.
Finally, in 1865, all slaves were emancipated.
The Republic of Louisiana is a unitary Republic and is divided in Departments, each department is further divided in Municipalities.