New Orleans will be a New York equivalent to the rest of the CSA: the wealthiest and largest single city, with the largest minority populations and a city which would also have some fairly standard and traditional racial tensions. Louisiana would carry on with its OTL-style gap between Anglo North and French-influenced South, though quite a few of its cities and railroads which IOTL were built by carpetbaggers will never be built in a CSA ATL, strengthening New Orleans even further in an imbalance over Louisiana in particular as opposed to the CSA as a whole. Louisiana will definitely be exceptional even more in the CSA with its civil law basis as opposed to common law, though it will be more under-populated and under-developed in a CSA setting than it was in the USA. It will also be distinctive in having its slave economy built around sugar and it *may* become another center of food agriculture in the form of cattle-raising as has happened in Louisiana IOTL.
Louisiana in short would be the CS California with a New York City equivalent as its biggest city, which is a combination without any real equivalent in an ATL USA. Shreveport may or may not develop depending on what happens with the Red River, Alexandria probably develops as per OTL. Lake Charles may well develop as a center of the lumber trade as it did IOTL though it may be more Cajun than IOTL. Louisiana's presence and significance as an oil state might well tilt it further in the direction of commerce for the CSA, which would be a potentially explosive combination in *any* CS political situation as Louisiana may well start claiming its resources in terms of sugar, commerce, and oil and natural gas will demand it receive concessions from Richmond Richmond won't want to give....