Prior to 1803, slavery existed in the Louisiana territory and its settlements such as New Orleans and St. Louis, but was regulated under the laws and customs of Spain (as I understand, the brief return to French control had not been in place long enough to see substantive change from the past 40 years of Spanish legal control, although at least there was French cultural impact, certainly). To be sure, being enslaved is awful any way you cut it, but from what I have read, there were nevertheless stronger legal protections for the enslaved persons under Spanish law than they would experience under American jurisdiction, and similarly, persons of color who were free, even if formerly enslaved themselves, were at least somewhat more accepted in society as compared, again, to the cultural mores that would come with the Americans. So that is the core of the question.
I'm especially interested in the changes, and more importantly, how quickly they came about. Were the slavemasters previously invested in the 'way things were', and didn't change very quickly even though the law changed, or were they mostly eager to transition to the 'American' style of enslavement?
Similarly, for free people of color, did cultural changes in their treatment mostly come about from Americans either newly arrived or newly empowered, or did the Spanish and French people of the region similarly adopt more "American" views on racial relations?
Additionally, how varied was it geographically? I know that in New Orleans there was at least some degree a holding over of the cultural treatment of the free black and mixed-race community so that it is generally held up as something of an anomaly in the South for antebellum race relations, but was this also true further North in settlements such as Baton Rouge or St. Louis? In the latter especially I know that there was a cultural holdover for a time but it seems to have been much less enduring.
Full disclosure: I am copying and pasting (with some adaptations) another answer that I provided some weeks ago now. It only partially answers your question, but I figure a partial answer is better than none, and I'm not knowledgeable enough about the enslaved population to answer the first portion of your query. I can help a little bit with the latter part though, particularly in regards to American views on racial relations vs. traditional colonial ones.
I'm not a historian, but I'm a Louisiana Creole who's very interested in this kind of thing, so I'll give what I know in the hopes of guiding you in the right direction.
I can also help with your last question by saying that New Orleans is not unique: Most of the following information pertains to people all across South Louisiana.
If you want any clarification, just respond or message me and I'll do my best to provide further sources or point you to where you might find more information!
Anyway, on to the answer:
One of the most obvious changes lies in the stark black-white dichotomy and the infamous one-drop rule, which are Anglo-American concepts that did not exist in Louisiana prior to the Purchase (or, from a Creole perspective, the Sale). They was lawfully and informally imposed by white migrants from other parts of the still relatively new United States over a period of several decades.
This has greatly damaged traditional Louisianian cultural identities, and this damage is still very strongly felt today. The most obvious casualty is the "Creole" identity, which is often used today to incorrectly refer to anyone of mixed race. "Creole" was not, and never has been, a racial identity. It is not a racial categorization. Anyone who was natively born in Louisiana during the colonial period, or descended from the same, was Creole. Purely French, purely Spanish, purely Acadian, purely German, purely West African, partially mixed, largely mixed—totally irrelevant. P.G.T. Beauregard and Kate Chopin are well known white Creoles, as is the French painter Edgar Degas (whose mother was a Louisiana-born Creole). Likewise, Beyoncé Knowles is a Creole of mixed race, as was Homer Plessy of Plessy v. Ferguson. Viewing the identity through a racial lens is a sign of Americanization.
The sad fact is that the Creoles of color were essentially not given much of a chance to resist the tide of Americanization, which proved to reduce and demote their place in society. Calls to resist basically went unheard. Some white Creoles tacitly supported their tactics, but not to any great extent, as their own personal interests demanded that they integrate with the white Americans. Of course, as Americans treated Creoles of color with disdain, they were not allowed to exercise much political power. Having the advantage of superior education, however, allowed Creoles of color to attempt to defy the new status quo better than new freedmen in other parts of the American South, and indeed many efforts to promote Civil Rights in the 1800s came from Louisiana Creoles of color. (See Desdunes, Plessy, etc.) But they were steadily disenfranchised thought the late nineteenth and early twentieth centuries.
This strategy partially had to do with the Anglo-American racial ideology, but it was also part of a concerted effort to Americanize a people who were potentially problematic. (This is why they took steps to stamp out the French language as well.) Educated gens de couleur libres—free people of color—posed a threat to the status quo in other parts of the South, as they essentially subverted American ideas of what people of African descent could and could not be allowed to do. And while no serious historian could claim that pre-American Louisiana was by any means a color-blind society, there is some historical evidence that suggests a certain amount of solidarity between Creoles of all racial backgrounds against Americans. After all, the Creoles spoke the same language (usually French) and practiced the same religion (Catholicism), neither of which the Americans did or even frankly approve of. The Comité des Citoyens, which encouraged Plessy to defy the law by sitting in a "white" train car, was a Creole organization that included whites and blacks alike. Rodolphe Desdunes, a prominent Creole of color activist and poet, once described the discrepancy between Creoles and Americans as:
"One hopes, and the other doubts. Thus we often perceive that one makes every effort to acquire merits, the other to gain advantages. One aspires to equality, the other to identity. One will forget that he is a Negro in order to think that he is a man; the other will forget that he is a man to think that he is a Negro."
It might also be worth mentioning that Beauregard, the Confederate General, later recanted some of his more racist views and campaigned for increased rights for those of African descent—enough so that Victor Rillieux, a blind Creole of color poet who wrote many poems about Civil Rights advocates, provided a eulogy for him: a man who had once fought for the right to enslave people of African descent. This is a uniquely Creole situation, and while I'm now veering into guesswork, it is difficult to imagine this sort of scenario playing out elsewhere in the Southern United States.
This shared sentiment began to fall apart in the early 1900s, when white Creoles began to fear that, to their now-powerful American neighbors, their Creole identity implied racial "impurity." They responded by arguing that only whites could truly be Creole (see the writings of Alcée Fortier and Charles Gayarré for prominent examples). Then, when this tactic failed, they responded by abandoning their Creole identities altogether. In the mid-1900s, when the Cajun-craze came about and everyone wanted to be Cajun, rural white Creoles essentially switched identities to one that was less racially ambiguous (so says historian Carl Brasseaux). This is why relatively few white people today claim to be Creole. But they are. In fact, all Cajuns are technically Creole according to the early definitions, and there is some evidence that at least certain Acadian descendants identified as such. It was a subcategory, not a distinction. If you read French, you might find this study interesting, wherein several white Creoles complain that their identity is being eroded by "Cadjins" (Trépanier, Cécyle. "The Cajunization of South Louisiana: Forging a Regional Identity." The Geographical Journal, Vol 157, No.2 (July 1991), pp 161-171.) Awareness of the original identity is slowly growing stronger, too, so there is perhaps a slow restoration going on.
So while I know this does not fully answer your question, I hope at least some of the information there will be interesting.
As an aside, I have been told that, just as white Creoles were pressured to abandon their identity by white Americans, some black Creoles are dissuaded from identifying as such by certain non-Creole African Americans because they see it as a cop-out or denial of their "black" identity. Again, I have not experienced this myself because I am not of African descent, and I can't prove it because I have no scholarly resources that state it, but I do know Creoles of color who've said this, and you do run across comments on Facebook or Youtube that seem to support this assertion. If you remember when Beyoncé's "Formation" was released a few years ago, or if you care to do a Google search, there were quite a few non-Creole African Americans who vocally disapproved of Beyoncé's mentioning of her créolité. I thought I'd mention this because it shows that the effect of the handover, and the consequent erosion of these colonial identities, continues even today, and not always in a political context.