Traveling from London to Normandy to Paris?

The northbound train out of Paris leaves from G. Lazare, not G. Lyon.

We've done it two ways. One is the Eurostar to Paris then get from Gare du Nord to Gare du Lyon I think, for a train to Caen, about 2 hours. We picked up our reserved rental car right across the street from the Caen RR station and drove about 15 miles to Bayeux and stayed there. We chose Caen over Bayeux because the car rental agencies are quite handy and open later most days.
Another way is to email Aquacars in Portsmouth to fetch you to Portsmouth, spend the night, and catch the morning ferry to the ferry port at Quistreham France, then the bus to Caen and pick up a rental car. We enjoyed both, but the Paris to Caen via train was simpler.

If you take a Brittany Ferry from Portsmouth to Caen (Ouistreham), you can depart in the morning, in the afternoon, or travel overnight. You can take an early train from London to Portsmouth in time to catch the morning ferry. If you're going to take a guided tour of the Normandy beaches, you don't need to rent a car. Take a bus from Ouistreham to Caen and the train from there to Bayeux. Spend the night in Bayeux. After your visit to Normandy, take the train to Paris.