Officially, there is no such place as the Place Saint-Paul in Paris. Nonetheless, to the citizens of this 4th-arrondissement neighborhood, the Place Saint-Paul is a real place near the Saint-Paul metro station and the Saint-Paul-Saint-Louis church. Here, almost in front of the church’s north-facing doors, the Rue Saint-Antoine meets the Rue de Rivoli at a narrow angle, forming a triangular island to the west of the intersection where there are trees, benches, kiosks, an entrance to the Saint-Paul metro station, a carousel for children, etc. Unofficially, this sliver of ground in the middle of traffic is the Place Saint-Paul, but most local people will tell you that the Place Saint-Paul extends a few tens of metres into the neighboring streets as well.
Perhaps a workable definition might be: the Place Saint-Paul is any place where either the Saint-Paul-Saint-Louis church or an entrance to the Saint-Paul metro station is within sight. If so, then the portions of the streets closest to the Rivoli/Saint-Antoine intersection would be included: Rue Saint-Paul, Rue de Turenne, Rue de Sévigné, Rue Malher, Rue du Roi de Sicile, Rue Pavée, Rue Francois Miron, Rue de Fourcy, and Rue de Prévôt.
Both the "square" and the metro station take their names from the local church, the Church of Saint-Paul and Saint-Louis. The area is also called "Métro Saint-Paul". A hotel nearby, perhaps acknowledging the unofficial nature of the “Place Saint-Paul” name, calls itself "Hôtel de la Pointe Rivoli".