Best is taking the train from Brussels to Bruges instead of a car. Is faster and much more convenient, the historic center of Bruges is about 15min walking from the train station. No worries this way about finding a parking or traffic jams mostly around Brussels.
I have driven several times in recent years up and down from my home near Bruges to Normandy. But I have my own car, in your case if you want to drive it’s best to take the train to Lille in France and rent a car there for the drive to Caen. Lille is an easy train ride from Brussels. In case you want to leave from Bruges you can take there a local train to Lille with a change in Kortrijk.
According Viamichelin you can do this following the A1 (direction Paris) and A29 (direction Amiens and Pont de Normandie near Honfleur) in about 4h and 11min. But that’s in theory. So no delays, no reststops, waiting at toll gates, driving through Lille and Caen, etc. Think more about 6 hours or maybe a bit more. If you don’t combine it with sightseeing it will be for the rest a boring experience. The scenery is with large stretches of agricultural land in general not so exciting.
Most of the time my first stop is in Arras drinking coffee and enjoying it’s hisitoric main squares. Further you can visit Amiens for it’s cathedral. The same for Rouen and it’s historic streets and the abbeys downstream along the Seine river. A stop in Honfleur is nice too and for instance Beuvron-en-Auge closer to Caen is worth seeing. You can’t all do this in one day, you have to make a selection.
Once I haven driven in one go to Le Mont-Saint-Michel and arrived late seeing it during sunset and later being beautifully illuminated. At that time the crowds are gone and the huge car park free and the shuttle to the island too. But check if the first is still free as it can be changed in the meanwhile.
So with some sightseeing think about a whole day you are on the move. Without sightseeing it’s better if the expences of travelling by train are comparable. You can use the Belgian website: SNCB International https://www.b-europe.com/EN for planning and tickets. As highspeed trains are involved book as early as possible, but think with four travellers anyway much more expensive compared to a car.