] There was very definitely an impediment to it (see my post citing the Catholic Encyclopedia on consanguinity in this thread). Napoleon was very powerful, however, and probably would not have had any difficulty obtaining a dispensation from the pope, who, like the Emperor of Austria, found it necessary to placate him. Politics!
This is the quote from Monica Stirling's book "Madame Letizia:
"When Napoleon decided to repudiate Josephine his brothers and sisters had hoped he might marry Lucien's daughter Charlotte and thus consolidate the family's power. (Such a marriage would have been permissable and not, at the time, unusual)."
I do realize that this was in France of a Corsican Catholic, but it is the same time frame as Jane Austen, and does shed light on how the rules of consanginity were regularly flaunted.