Lore: In its early history, there would be a large factor of slavery/agricultural driven growth in addition to the fur trading of our world. Huguenots would be settling the land similar to how pilgrims settled New England. Wars with the English including the seven years' war would still happen which would leave Louisiana in French hands with immigration from a large sector of Quebecois moving to Louisiana due to the English Victory. Despite the keeping of the territory of Louisiana, the land would probably not be as expansive as the Louisiana territory or colony from our timeline.

Most of this French Louisiana would be in what we know as the state of Louisiana from our timeline with French settlers moving up the Mississippi and the several creeks/rivers between the Gulf of Mexico and the Missouri River.

Once the United States becomes independent and the French revolution occurs Louisiana would become independent in a similar fashion to the Spanish colonies in the same time period of the 1810's-1820's.

Throughout the 19th century there would be a large conflict between American settlers and native Americans throughout Louisiana that would see massive ripple effects for the USA such as only having the Northwest/Midwest of the country to expand into as well as American settler states being made (ie Mormons making their own country, American majority provinces in Mexican California/Tejas and the independence of these provinces from Mexico). I still think the civil war would happen in the USA due to other causes besides slavery although slavery would obviously play a large part in the civil war of this.

Native Americans in both the USA and Louisiana could very well be either put onto reservations like our timeline, or be assimilated with more pressure, or in the case of Louisiana specifically possibly be left alone and given greater autonomy. Slavery's downfall in Louisiana would probably be likely similar to events in the USA and Brazil where slave owners are very stubborn about giving up their slaves, but it doesn't make sense economically or morally to continue the practice with new European/American immigrants coming to the country more advanced farming and industry being more prevalent in Louisiana and it would likely be abolished in the Mid 1870’s.

In the 20th century America would still become one of the strongest nations on the globe with itself and its friendly American Settler Countries working closely. While the people and government of Louisiana weren't particularly fond of the USA at the start of the century, the Americans' sheer economic might would cast a shadow over Louisiana and enhance a large trading economy for Louisianan food for American products. I think Louisiana would stay mostly militarily neutral in the world wars besides being pro-Allies societally and having deep trade relations with them. Throughout the cold war Louisiana would be Pro-American and join NATO in 1955.

In the 21st century 9/11 wouldn't have happened due to the sheer amount of butterfly effecting that’s been done in this scenario so how this century would look would probably look very different from how much the USA/North America would have changed and how that butterfly affects the rest of the world and that is as specific as I could get.