This one's an interesting thought, and I'm more interested in a certain particular facet of this than anything else that might come up--canals and inland waterways.
I think the starting scenario (not particularly plausible, I admit, and I'm ignoring lots of butterflies and making it deliberately minimalistic) is necessary to lay out here so we can discuss this topic, so let's just say that France for some reason intensely settles Louisiana starting in the mid-17th century. The main competitor to France is Britain, who goes with early Trans-Appalachian settlement and also takes Florida and Mobile to help facilitate that settlement. Spain is a lesser competitor, and most all of Spanish Tejas is conquered and nominally under French rule. But France can never defeat Britain, who by the mid-18th century has expelled as many French as they can (Acadian style) from the east of the Mississippi, leaving the borders at the OTL 1763 borders. The final border change in the east occurs in 1783 when France claims an outlet on Lake Superior at OTL Duluth and surrounding lands in exchange for helping the British colonies gain independence. Louisiana gains independence in 1790 because of some some alternate French Revolution. I'd write more, but let's ignore what happens elsewhere in North America. We'll assume relations with the *United States are cordial and the Mississippi River is effectively internationalised.
So now that we have the setting laid out, let's also assume that Louisiana enjoys a period of canal mania, canal supporters tend to win during internal political debates, and ITTL railroads are delayed by maybe ten years, so we can have a canalwank. Where are these canals likely to be? Is the OTL system of inland waterways west of the Mississippi a good clue as to how the layout would look? But what about ones which don't exist OTL? Can you build a canal linking the Great Lakes and Mississippi watershed with one end at Duluth and the other a town on the Mississippi? It looks like it would be pretty challenging, if its even doable before railroads. The results would mean Louisiana could bypass US control of any Chicago Ship Canal.
The other big one--how far upstream can the Missouri be made reliably navigable? Bismarck? As far as Great Falls?
I'll let your minds run wild. Note that this could apply to the US too, but I think this version of an independent Louisiana or any other state with a similar history is far more likely to embark on these sorts of engineering projects.