The most convenient way to get from Paris to Honfleur is by train. The TGV Paris-Deauville-Trouville high-speed train makes three daily trips from Saint-Lazare station. Just over two hours on the road and you are in blessed Normandy. Honfleur does not have its own train station, so get off at Deauville-Trouville station and take buses 20 or 50. Besides Deauville, you can take tickets to Le Havre, Pont l'Eveque or Lisieux stations. The distance from them to Honfleur is about the same.
Please note that TGV trains will cost only 30 EUR if booked in advance. By paying a few euros extra and booking tickets with seats, you will save yourself from the crowds on the train, especially on weekends and holidays.
Don't forget to validate your ticket when you enter the platform before boarding to avoid being fined for fare evasion.
