Jamie,
Could you provide a few details on what you want to see in both Paris and Normandy? That will have some bearing on how long to stay in each location.
The most direct and easiest route is that suggested in the previous post. It won't necessarily be cheap though if you're using the EuroStar. The route would involve London St. Pancras to Gare du Nord, Metro from there to Gare St. Lazare and then train to Bayeux. I'd suggest staying at least one night in Bayeux, especially if you're planning on taking any D-Day tours. A visit to see the famous Bayeux Tapestry would also be good.
I would probably visit Normandy first and then stop in Paris for a few days on the way back. It would be a fairly easy trip back to London from there (again via EuroStar). Using budget air may be a bit less expensive initially, but when all is considered it would probably be more of a hassle for that short distance and would probably involve more travel time than taking the train.
Happy travels!