If Napoleon had conquered Britain as well, you might have had access to all those supplemental marriage documents like they have in the Netherlands ... (incl extracts of birth or baptism documentation)
It is interesting that we've got so much on the background of that couple, but that that we still don't know whether John
Augustus Anthony Bernard (1837 Dover UK) = John Anthony Bernard (1847 New Orleans USA). They were either different people after all or there would have been - most likely - a legal reason. The other thing that has intrigued me is the seemingly lack of legal children, but at least 2 children out of wedlock.
(I'm just going to throw out a few ideas)
The first wife (Alexandrine Poulain) dies somewhere in 1831 and the wife's age on the 1845 passport fits for Eleanor Goddard. It
seems that there is no problem there, but maybe there had been another marriage after Alexandrine and before Eleanor that we haven't found yet.
The Bernard family appears to have been fairly wealthy and would have had to make sure that legally everything was in place (especially with 2 "natural" children hanging around). St Mary the Virgin in Dover is an Anglican church. Maybe this was an issue in Roman Catholic Louisiana and therefore they had a state marriage as well? Or, did an Louisiana resident have to legally register his/her foreign marriage before it was recognised? Of course they could have just lose their original marriage papers or maybe there was something wrong in the 1837 certificate that would have made it invalid ...
Maybe someone else can think of other possible reasons