Best way to travel Bruges to Normandy
You'll have to define "best".
It depends if you intend to travel by car around Normandy, or not.
If you travel by car, then take the train to Lille + rent a car in Lille. The drive is long-ish (unless you stop in northern Normandy, i.e. Dieppe, Etretat...) and not that interesting, but saves you the hassle of changing trains in Paris.
If you use public transport or guided tours in Normandy, then take the train through Paris (EDIT: that involves a change of stations, from Nord to Saint Lazare).
Note that trains through Paris likely involve a change of station in Paris. Your next destination after Normandy may be a factor as well. How are you getting to Bruges? Alas, the fact that both places are on the English Channel have little to do with land transportation.
The route suggested by Lisalu avoids the need to transfer between Nord and Saint Lazare stations in Paris, but is only viable (1) if you find a good connection - tricky, and the SNCF booking engine won't show you that route by default and (2) if your Normandy destination is indeed Rouen. Bayeux is on another railway branching out of Paris, it can be reached from Rouen but it is cumbersome.
We drove from Lille to Normandy several years ago and this is now on my "never again" list. It was a VERY long drive, lots of tolls, and not that interesting as another poster commented. Went back the next year and took the train to Bayeux, then rented the car there. That was much better.