LeopoldPhilippe said:
Emperor Napoleon I and Empress Josephine did not have children.
Eugene de Beauharnais was the Emperor's stepson. Eugene was also the Emperor's adopted son.
Suppose Napoleon I recognizes Eugene as his heir. Napoleon does not divorce Josephine.
Suppose Napoleon reigns until 1821.
Eugene becomes Emperor of the French. He lives numerous years past his actual 1824 demise date. What happens then?
Eugene seems to have been pretty well liked compared to Napoleon. He got along very well with his wife Augusta Amelia of Bavaria, which in turn allowed to buld strong ties with the Wittelsbach. I also remember him getting along pretty well with Alexander I of Russia. Also, given who he was able to marry his children to OTL, it seems he would probably be accepted among the royals of the time.
That said, a lot of this doesn't depend on him but on Napoleon himself. Why Napoleon didn't divorce Josephine, why he stayed in power up to 1821 and what's the situation in Europe at the time of Napoleon's death are the key questions to determine how Emperor Eugene I would be viewed.
The best case scenario implies that Napoleon has made peace with Britain (hardest challenge), that the troubles in Spain never happened or were crushed, that Austria isn't a possible threat and that the peace of Tilsit with Russia holds. In which case, Eugene pretty much inherits the glory of Napoleon and has his place among the royal families of Europe. But achieveing this best case scenario is extremly hard, especially because we're more or less needing the British to accept French hegemony on the continent, something they would never agree to unless their hand was forced, they get a pro-Napoleon government (there were a few poiliticians ready for that in Britain, but there were a minority) or Amiens holds (but that potentially buterflies the French Empire).
Janprimus said:
Given how supportive Napoleon was for the rest of the Bonaparte family, I suspect he might prefer naming one of his (Bonaparte) nephews as his heir instead.
Not so sure. Napoleon was pretty close to Eugene de Beauharnais, which is why he adopted him. Plus, Eugene was always one of the most loyal supporters of Napoleon as well as one of his best subordinates (it seems Eugene is even underrated for his military accomplishments). Besides, Napoleon had already been prepared to made Eugene his heir for the Kingdom of Italy if he had no second son: that's one of the reason Eugene was granted the titles of Viceroy of Italy and Prince of Venise.
Having Napoleon name Eugene his successor for the French Empire doesn't seem that unlikely in these conditions.