You could weigh the density by population (effectively giving you population²/area?! I'm not saying this is a good idea), and you'd get a top10 of Paris, Barcelona, Madrid, Bucharest, Berlin, Athens, Milan, Brussels, Vienna, Naples, which despite the slightly bizarre metric seems a more sensible ranking (Emperador is at the bottom rank), and which, to be fair, also features two Spanish cities.
But again, it's kind of a pointless endeavor, because of the arbitrary nature of the boundaries chosen -- why Paris and not Paris metro? etc. I guess ideally you'd have a function density(person) giving you the population density of any given person and you'd want to look at the distribution of that function, specifically the average per country of that function.