Can you tell me how the zone system works?
The Paris fare zones affect multi-use passes & tickets that you can purchase, allowing you to choose the coverage of fare zones needed on your Navigo Day pass for example.
See the following article for an in-depth explanation of Paris fare zones.
By default, a weekly Navigo Pass you buy will cover all zones, 1-5. If you're arriving by airplane to Paris, you will need all 5 zones of coverage to cover CDG & Orly airports.
If you're arriving to Paris by train at Gare du Nord, you don't need a week pass, but day passes and you have no plans to travel outside of central Paris, then you could buy a 1-2 zone Navigo Day Pass or Ticket Mobilis and save money with the reduced coverage.