Point Zero.  It is located about 10 meters WNW from the center portal of the Cathedral de Notre Dame de Paris.  The inscription says "Point zero des routes de France".  When you see a roadsign telling you you are 137km from Paris, that distance is measured to this point. 

This is the center of Paris.

Looking south we can see the beginning of the Latin Quarter a few hundred meters away.

When we walk around behind the church to the east we can see Île St-Louis.