A sizable portion of Paris residents live in public housing:

This summer, when the French capital welcomes upward of 15 million visitors for the Olympic Games, it will showcase a city engineered by government policies to achieve mixité sociale — residents from a broad cross-section of society. One quarter of all Paris residents now live in public housing, up from 13 percent in the late 1990s. The mixité sociale policy, promoted most forcefully by left-wing political parties, notably the French Communist Party, targets the economic segregation seen in many world cities.

“Our guiding philosophy is that those who produce the riches of the city must have the right to live in it,” said Ian Brossat, a communist senator who served for a decade as City Hall’s head of housing. Teachers, sanitation workers, nurses, college students, bakers and butchers are among those who benefit from the program.

Making the philosophy a reality is increasingly hard — the wait list for public housing in Paris is more than six years long. “I won’t say this is easy and that we have solved the problem,” Mr. Brossat said…

City Hall has a direct hand in the types of businesses that take root and survive in Paris because it is the landlord, through its real estate subsidiaries, of 19 percent of the city’s shops. Nicolas Bonnet-Oulaldj, the city counselor who oversees the city’s commercial landholdings, said his office is constantly studying neighborhoods to maintain a balance of essential shops and limit the number of chains, which can usually pay higher rent.

Three related reasons come to mind for why this would not happen in an American city, even with significant needs for housing:

1. A supposed free market approach to housing. Americans prioritize policies and programs for single-family homes, not denser urban housing with subsidized rents. Why should public housing take up valuable real estate that would go for much higher prices on the open market?
2. Many Americans think public housing has already failed in the United States. The story might go like this: the limited project that began in the first few decades of the twentieth century led to disastrous high-rise public housing projects in big cities and a subsequent retreat from public housing (shifting to providing housing vouchers).
3. Less interest in centralized planning and government control. Would Americans want the government choosing housing and business opportunities in major cities? You mean Paris is not organically developed?

Overall, American cities pursue market approaches to social issues.