Paris is divided in 20 arrondissements and their number spiral out from the middle of the city. That is why arragement of arrondissements is said to be placed like a shell of a snail.
The ZIP code is 750XX. XX corresponds to the number of the arrondissement in 2 digit numbers (for example: 75008 refers to the 8th arrondissement, and 75017 refers to the 17th arrondissement), Except for the 16th arrondissement which is divided in two: 75016 for the south and 75116 for the north. With this ZIP code you will be able to get your bearings easily.