Unlike basically anywhere else in the United States, Louisiana has historically hosted a vibrant, influential, and financially solvent community of Creole people of mixed French and African descent. The whole existence of this community defies a lot of our expectations about race in the USA, but these people are essential to the history of New Orleans.
So how did Creole people react to Louisiana's decision to secede from the USA in defence of slavery? Were these people generally Unionists or did many work with the new government? Did many Creoles own slaves themselves?
Because New Orleans was probably the biggest port of the Confederacy, this community was probably pretty important during that period.
I'm going to allow somebody more qualified than I answer your question, but I will insert a note: Your definition of Creoles as Louisiana's free people of color is incomplete. Technically, you're speaking of Créoles de couleur. To be Creole during the time period, one needed only to be born in the colony of the Spanish "Luisiana" / French "la Louisiane" as opposed to being a European/Canadian immigrant or a slave brought directly from Africa, and thus there were and are French Creoles, German Creoles, Spanish Creoles, African Creoles and any mixture therein. The white P.G.T. Beauregard, an aristocratic Confederate general during the Civil War, actually bore the nickname "The Little Creole" among his Américain peers. The "white francophones = Cajuns" and "black francophones = Creoles" dichotomy is a relatively recent (and incorrect) invention and does not reflect how people at the time of the Purchase actually identified themselves. Anyone can be Creole, regardless of their ethnic background.
If you want to more about Creoles of color, Emily Clark's The Strange History of the American Quadroon might interest you, as it primarily focuses on New Orleans.
Some Creoles of color did indeed fight for the Confederacy, most notably the 1st Louisiana Native Guard, which was founded and manned by volunteer Creoles of color, mainly from New Orleans. They were militiamen more than anything else, but still possess a symbolic significance for New Orleanians. Many Creoles of color did indeed own slaves, but for the most part, they were motivated by their general discontent regarding American ideals entering Louisiana, because Colonial Louisiana did not adhere to the One-Drop Rule; the idea that all whites were superior to all blacks (and that even a single African ancestor qualified you as "black") relegated Creoles of color to a position inferior to that which they had held under French and Spanish laws. I won't go into detail because, again, I am not an expert on the topic.
Bennett Wall's Louisiana: A History and Fertel's Imagining the Creole City might also give you the answers you seek, although these texts do not exclusively focus on Creoles of color but rather on Creoles and non-Creoles as a whole. When discussing some of your questions, however, the status of Creoles is better seen as pre- and post-Louisiana Purchase rather than pre- and post-Civil War.
I'm sorry I couldn't be of more help (I can share further opinions and facts, as this is a topic that I enjoy reading about, but I have a poor memory for exact sources and by the rules of this sub am probably not qualified to recount much more than I already have), but I hope I was able to point you in the right direction.