So it looks like it's happening very soon, most likely the coming season.
The first cross-town rivalry in Ligue1.
Paris FC vs Paris Saint-Germanin
As some may know, Paris FC is in Ligue2 and have been bought by Arnault (Agache Sport, which even less people know had enquired about both Milan and Inter in recent years) and are collaborating with the Red Bull Sports group, which I assume means they'll gain a lot from their scouting network and Jurgen Klopp is part of that organization now as well, so we may see hiim coach this Paris team soon if he's willing to take such a role.
It's going to be crazy if they invest as expected and will cause cataclysmic effects in PSG's dominance.
And unlike PSG who at least showed us something in the 80s, 90s and even 00s, Paris FC are pretty much nobodies. They share some history of mergers and splits with PSG, but that's about it.
They're currently sitting joint 1st (top 2 are automatic), 5 points clear of 3rd spot (playoff) and 7 points clear off of 4th spot which would keep them in Ligue2.
Maybe within 2-3 seasons, assuming they reach European spots, we'll probably hear Parisian sirens for our players and it won't be just PSG...