I came by car but I left for England on this ferry. I love travelling by boat. It gives you a different perspective of your surroundings and there're no traffic lights.
I spent a lot of time exploring the town by car. It took a little while to get used to the rules about right of way. Most of the time I was parked by the beach walking up and down and around the port. There was a skateboard park that was fun to watch at the beach also.
I have used a car leaving from Caen on the way up to the North, before going to Le Havre, take a look at Hounfleur, you'll fall in love with this town, the harbour and downtown area are something. Check, you'll be surprised.
If you're travelling west from Le Havre make sure to go over the Pont du Normandie. It's a huge bridge! It's an amazing view when you approach it!!!
It's unfortunately a toll bridge as well. It costs 33 Francs (approx. 5 Euros) to drive over it.
Have a look here: http://www.ferrybooker.com/ferry_port/le_havre.asp
There's a map there which shows the British Terminal and the train station.
It should not be more than 1.5 kms (calculated via www.viamichelin.com) which is walkable if all else fails.
Another website says that there is taxi service at the station. It's a 5 minute ride and costs approx. 8 euro.
Google 'le havre taxi' and you get a list of companies and phone numbers:
Radio Taxi Le Havre +33 2 35 25 81 81 -
Lemaire Joël +33 2 35 41 25 88 -
Jouen Philippe +33 2 35 44 34 13 -
Eurl Lemaure Taxi +33 2 35 46 39 85 -
Maze Jean Claude Andre +33 2 35 48 70 96 -
Brakni Karim +33 2 35 49 33 07 -
France Remise +33 2 35 25 12 33 -
Le Bourser Franck Yves Jean +33 2 35 25 12 33 -
Le Bihan Jean Marie Rene Gustave +33 2 35 42 25 52 -
Lecoutre Michel - +33 2 35 46 13 38 -