This is a really complex question because of the different social groups in Louisiana at the time. Cajuns are a specific sub-group -- do you mean Arcadians in Louisiana in specific, or all Francophone Louisianans, including people of colour? Just white Francophone Louisianans? Just Free Creoles of Colour? Because the answers are very specific to each, and I want to make sure I'm answering about the people you really want to know about.

Generally speaking, succession was met with mixed feelings. Planters who owned a great many slaves or anyone in the slave trade was in favour of it, as were a large portion of white Francophone Louisianans, who never felt much like part of the United States in general. New Orleans was lit up with a parade when Louisiana left the Union, the 6th state to do so, and the French Quarter turned out French-speaking Creole units for the Confederate Army -- including the 1st Louisiana Native Guard, a regiment entirely consisting of free men of colour, which formed at the Catholic Institute in New Orleans in 1861. Louisiana law changed in 1862, restricting the right to bear arms to white men only, and the units were disbanded. Some of the soldiers left for the Union. Others just went home, as by 1862, New Orleans was captured and the war was losing popular support on the Western Front.

Cajuns is a pretty broad group as well. Some did become wealthy after coming to Louisiana from Canada, and they were generally in favour of the war, as they were largely sugar planters with slaves. Most, however, were not wealthy and did not support succession. Their trepidation was proven wise as military action across Louisiana destroyed many Cajun farms and left them destitute. Reconstruction and the strong presence of Anglophone Union Army troops in Louisiana also did a lot to marginalise Francophone Louisianans, pushing them to the edges of society and making them a cultural minority and increasingly, a tourist curiosity after the war.

If you're interested in the Native Guard, a good book to start is: Hollandsworth, James G., The Louisiana Native Guards, LSU Press, 1996.

For Louisiana in the war more generally, I like: Ayres, Thomas. Dark and Bloody Ground: The Battle of Mansfield and the Forgotten Civil War in Louisiana (2001) and Pierson, Michael D. Mutiny at Fort Jackson: The Untold Story of the Fall of New Orleans, Univ of North Carolina Press, 2008.

And an overview of Louisiana more broadly that touches on slavery, secession, and the war: Campbell, Anne. Louisiana: The History of an American State. Clairmont Press, 2007.