Eventually, like Texas, it gets absorbed into the US. Being that Britain and France were colonial competitors, Canada would never absorb Lousiana. Mexico would have lost Texas ATL so it seems to me Lousiana would go the same way eventually. Perhaps, it would just be purchased at a higher price or it would be part of a war that breaks out after the Civil War during the Franco Prussian War.
Speaking of the Civil War, I wonder if this ultimately delays the war as SOuthern States would have expanded as OTL besides Arkansas and possibly Lousiana (though a much smaller version may exist with the purchase of New Orleans.) The Union would lose Iowa, Missouri, Minnesota, Oregon, and Kansas as votes in the Senate. California would be a state, however presuming the Mexican American war still happens.
This means slavery probably ends in the late 1870s or early 1880s, where a law essentially buys all the slaves at market price and frees them...ironically, this is probably cheaper than a war and a lot less deadly. It also improves the SOuth's economy long term and perhaps prevents sharecropping.
Lousiana as a territory, without New Orleans though is completely useless. How would the French defend it? Establish ports on the Pacific? Get real!
France likely selols the Lousiana Purchase a decade later. Maybe for another 15 million. It is just more fun to think about it hanging on later as a French territory longer.