In order to get a feel for Paris, you will need to visit all 20 of its arrondissements or municipal districts. These districts form a clockwise spiral from the middle of the city. Medieval Paris included the 1st through 6th arrondissements – abbrieviated (eme) or (e). The Renaissance and early Modern period included the 8th to 11th eme; and the industrialized city included all twenty arrondissements. Each arrondissement has its own mayor; is numbered using Roman numerals; and the last two digits of Parisian postal codes indicates the arrondissement (75001 to 75020). Each arrondissement is also subdivided into four quartiers and each quartier contains a police station. The first twelve arrondissements created by law on October 11, 1795 as a means of controlling militancy during the French Revolution. The size of Paris increased between 1859 to 1860; and on January 1, 1860 Napoleon III, rearranged the new territory and increased the number of arrondissements to 20. The inner spiral (3-11) reaches around to the Bastille where the outer spiral (12-20) begins. 
As I share pictures and stories, I will try to remember to include which arrondissement they are in so that you will get a feel for the various neighborhoods. This map gives you an idea of the neighborhoods and how Paris developed.