Did the state of Louisiana regard the people in question as having been Florida residents at the time of the wedding?
I did the reasearch on for such a case.
I did not find any. Of course I could ultimatly find own if I kept searching however I doubt it.
The LA law I found indicated they would in fact recognize a FL cousin marriage. (ie Albert Einsteins marriage would also be recognized due to a grandfather provision)
Pretty much all the cases that do allow challenges are based on CHILDREN crossing state lines and then the parents having the marriages annuled. (ie 16 year old daughter ran away with 17 year old boy and came back to state where consent is 18)
Given absolute lack of cases to the contrary, a FL marriage by first cousins who are adults would be recognized in LA.