The possibilities of travelling there, though straight forward, are limited to ferry and road. This is also much the best way to visit the area once you are there, besides walking!

Le Havre (from Portsmouth)- just 15 miles away when you cross the huge Pont de Normandie.
(péage = 5€). Crossing time = 5 hours

Caen (from Portsmouth) – 47 miles and about 1 hour drive across Normandy (péage = 2,80€)
Crossing time = 5¾ hours by ferry or 3¾ hours by Fastcraft.