In this January 2018 report from the Fraser Institute, they pegged the average population density of Paris to be about 21,067 inhabitants per square kilometer (2014 population year). It is the second densest city in their report after Hong Kong, but the densest in Europe. By comparison, Vancouver sits at around 5,493 inhabitants per square kilometer (2016 population year).
Now, these are of course city averages. Some neighborhoods will be higher and some will be lower. According to a January 2018 study by Alasdair Rae -- who is a works in the Department of Urban Studies and Planning at the University of Sheffield -- these are the most densely populated square kilometers across Europe (or at least within the 39 countries that he looked at).
Paris, once again, comes in near the top with a peak density somewhere around 52,218 inhabitants per 1km square. The square in question is in the neighborhood of Goutte D'Or. And the only square within the study to come in denser is one from the L’Hospitalet de Llobegrat in Greater Barcelona (53,119 inhabitants per square kilometer).
