Not the same guy, but if a class of people have to move out of the city because they are being priced-out, they will not vote in this city anymore (but in their new city in the suburb), shifting the current political balance. The current Paris mayor is from the Parti Socialiste (left-wing / moderate left-wing - for France), and may get a lot of their vote from the working class people living in Parisian social housing. Therefor, they have an active interest in keeping them within the city.

The political theory is true but I have no idea if the people living in social housing do vote more for the current mayor though. So it is just theory.