Parisian region is filled with incredibly talented young players. Most of our NT players were born in or around Paris, and there are many others who go unnoticed for too long. Several of them are bought pretty young by french teams far from Paris (Pogba started in Le Havre for example, Mbappe in Monaco etc.). There's room for at least one or two other top teams in Paris if a smart manager with very good scouts start buying good prospects around here. So your idea is definitely not a bad one. But since nobody's done it, I tend to think there's something we don't know that prevents an opportunity like that.
What is the story with Paris FC and the investment in them? Are their owners trying to take them to Ligue1 and create another strong Parisien club?