What is easiest way from Zurich airport to Paris by train?
According to the Swiss Rail website (www.sbb.ch/en/) it is about a 5 hour journey. Zurich Airport has a train station built into it you will have to connect at either Zurich main station or Basel for direct trains to Pairs-Est station.
The Zurich Fluhagen (airport) train station is directly below the airport. Just escalator or elevator down to catch the train. Depending on the run you choose, you will change trains in either Basel, Zurich HB (main station), Geneva or Lausanne before proceeding to Paris. All train runs from Zurich to Paris will terminate in either the Paris-Gare du Nord or Paris-Gare de l'Est. I don't see any that terminate in the Paris St. Lazarre station. You can take a bus between train stations.
CLICK HERE to see a map of the Paris train stations.
When you get to Paris take Metro line 7 from Gare de l'Est to Opera. Transfer to Metro line 3 and take it to Gare St-Lazare.
Or if you don't want to haul luggage up and down the stairs, take either bus #26 or a taxi. It's a short ride.