London to Bayeux

Skip Paris go straight to Bayeux.
Take the Eurostar from London Pancras to Paris Gare du Nord.
Once in Paris take a taxi from Paris Gare du Nord to Paris Gare St Lazare train station.
At Gare St Lazare buy a ticket for the next train to Bayeux.I

I would buy the London to Paris ticket first at eurostar.com.

Travelling by train from London to Bayeux takes almost a whole day with a change of train stations in Paris.

Take the shortest route, like the invasion army did on D-Day, and take the night ferry from Portsmouth to Caen. Take a train in the evening from London to Portsmouth, sleep on the ship(saving a night in London or Paris) and arrive to the port of Caen in the morning. Bayeux is close to Caen, you can take a bus or train, uber, taxi or best of all rent a car since you'll need it to explore Normandy.

https://www.seat61.com/France.htm#London to Normandy

https://www.seat61.com/London-Paris-ferry.htm

karen, you have two great replies, the 2019 route, and the 1940 route (seasickness included at no extra charge.) You may get more help if you explain what your objective really is. Is it, perhaps, the Normandy beach sites? Is your trip primarily to England and you want to see something that "seems" nearby?

Of course hotels in Paris are expensive, but there are cheap hotels in Paris too, if you plan far enough ahead. Have you been to Paris before? I ask because it is one of the great cities of the world, and has much more to do (opinion) than Bayeux. One value of spending two or three nights in Paris is breaking up a rather tedious trip, not to mention the joy of visiting Paris.

We are doing that trip in a few weeks. I looked into all options (including flying from London) and ultimately decided on the train. We leave around 8:30am and get to Caen around 4. So yes it takes a day but we felt that would be the easiest option for our family.
Thanks~
Heather