European cities like Paris are much, much older than American cities like New York, and that age difference has led to many interesting differences in the layout of each city. For example, the wealthy population of America often live in suburbs away from the city while in Europe, the rich live inside the city. Why is that? It's because hundreds of years ago, there were no cars or trains to take people to the city. So people basically had to walk from where they lived to get to where they worked. Since the wealthy weren't about to walk far, they settled as close to the city centre as possible. If you look at an income map of Paris in the 1500's, you'll basically see different rings around the city centre with the closest rings being the wealthiest areas and the areas farther away being the poorest.
But still, everyone wanted to be close to the city. That's why the population density of European cities is so much denser than American cities. New York's population density compares more to Lyon, France than it does to Paris. That's because in America, cities were being built around the time when trains and cars could transport people around. Initially, those trains and cars were reserved for the very wealthy because they were expensive to use and buy. If you look at an income map of America around that time, you'll see the rich living near the railway stations of the past. So the rich could settle in suburbs because they could afford the means to get to the city.
It's a really interesting look at urban geography and how cities were built. The always excellent Wendover Productions goes deeper into it by looking at how crime in the inner city is much more rampant than it is in European cities and how that helped drive the wealthy away too.