Normandy Beaches

I think the train's first stop is Lille. Unless you want to drive, you're better off going in to Paris and getting the train to Bayeux, Caen or another town in that area. We've only done Bayeux and take small-group day tours. We are fans of Hotel d'Argouges, but there are other great hotels in Bayeux. Someone just posted a great link to tours in the last few days. Try typing "Normandy" in the search book on the home page and see if the link shows up there.

The quickest way is not via Lille but Paris.

France and French transportation are very much hub and spoke with Paris the centre of everything.

You will find it fastest to take the Eurostar (chunnel is an anachronism only used by a few people now, including Rick, but by very few on this side of the puddle) to Paris. Cross Paris and take the train to Caen which has car rental places next to the station. I suggest making Bayeux your base.

Are you OK on a ferry? Might find more to see by going down to a south coast port in England (Portsmouth, Poole etc) and go across the channel to Normandy from there (Cherbourg, Caen, Le Havre etc).

Just in case you are interested in a ferry, for a change last year, rather than taking the Eurostar, we took the train from London to Portsmouth, and took the morning Brittany Ferry across to Ouistreham (that may not be spelled quite right), then a bus into Caen. The bus ends at the Caen train station. The car rental agencies are just across the street. We rented a car for touring Normandy and Brittany. We enjoyed the experience and it was convenient. We eventually ended up in Quimper and took the TGV back to Paris.
If you take the Eurostar to Paris then a train to Caen, the rental car agencies are just across the street from the front door of the train station.