It can't be done unless you are superman/wonder woman.
Let's say you are willing to to be up at stupid o'clock in London to catch the first Eurostar of the day to Lille, the 6:47 (you need to be checked in, not in the queue but checked in, 45 minutes ahead, so arrive not later than 10 or quarter to 6.
That train loses an hour changing time zones and arrives at Lille at 9:30 Central European Time (or Central Daylight Time depending on your date). An hour to get the car (10:30) and start out of Lille onto the Autoroute system. 5 hours on the Autoroute and you can be at Arromanches or other beach by about 3:30 in the afternoon. Do you want lunch? Need to use a toilet? Add at least half an hour, so you are arriving at your first beach around 4. How much time do you want to contemplate and understand? How many beaches (there are 50 miles of them where the invasion happened) do you want to visit? Do you want to visit the American Cemetery? Or the museum. Closes at 6, last admission at 5:00pm. Things, especially if you haven't been there before, can be quite a long way apart.
So, as it gets dark around 7, you will want to finish the beaches and surroundings by then. Dinner?
Figure 3:30 to 4:00 to drive to Paris for an 11:00 pm (23:00) arrival. What time does the car rental place close?
You must have more energy than me.