Actually two of the 20 districts of inner Paris (the "arrondissements"), which you describe as a "historical preservation district writ large", are more densely populated than any districts in any Western city - except for Manhattan Community Board 8 and 2 districts in Spain [1].

The 11th and the 20th arrondissement both house more than 40,000 people per km2 (104,000 per sq mile), which is denser than any district of Tokyo by the way. If that's not dense, I don't know what is.

Incidentally, the 11th is not cheap in any way: buying a flat there will set you back 9000 to 9500€ per sqm ($1200 to $1270 per sqft) [2].

[1] http://en.wikipedia.org/wiki/List_of_city_districts_by_popul...

[2] http://parispropertygroup.com/blog/2012/real-estate-prices-p...