Car rental or train

Also, is there any advantage to returning the rental car to the original pickup location

There's no advantage in driving to Bruges from Paris. Trains are frequent and easy, and you don't have to worry about parking in a city where it's hard to find a spot. You might consider taking the train to Bruges, and then as far as Caen in Normandy. Then pick up the rental there.

We are planning this exact same itinerary, and we have decided to rent a car. We will rent the car at CDG, drive to Bruges via Vimy Ridge battlefield, park in Bruges at a free spot arranged by our AirBnB host, then drive to Normandy. We will then go to Giverny and drop the car off at Mantes-la-Jolie before taking a train into Paris (driving in Paris is to be avoided if possible).

There are very real advantages to renting a car over driving. Most important, you get freedom to stop wherever interests you, like WW1 battlefields, or just any pretty spot you see out your window - total freedom. And to travel around Normandy, you will want a car to get to towns and WW2 beaches. Also, renting is cheaper than trains if there are more than two of you.

If you rent a car in France, you can return it anywhere in France for little or no dropoff fee (at least with Europcar). If you rent in Belgium and dropoff in France (or vice versa), there are often prohibitive dropoff fees.

If we drive do we need an international drivers license?

If we drive do we need an international drivers license?

It depends on where you come from (which country issued your licence).
If your licence is from a non-EU/schengen country then for driving in France you need an IDP (International Drivers Permit) to accompany your licence and certify it as valid. One IDP for each licence.

Here's a compromise. Take the train to Bruges, then IC/TER train to Lille. In Lille rent a car and drive to Normandy. That way, you don't have to take a train back to Paris, change from Nord to St Lazare stations, then train to Normandy. Drive straight to Normandy from Lille, by-passing Paris.

I would follow Sam's suggestion.

You can take for instance the train from Paris to Lille and rent a car there to drive to Bruges. Like darrenblois already says contact the place you stay and ask for a good, safe spot to park the car. There are free spots outside the historic centre, as Bruges is compact likely you don’t have to walk that far. Next to the train station there is a big parking lot and costs €3.50/24h and I often (once a month) park my car there overday and I think it’s safe during the night too, but ask your host to be sure.

A car makes only sense to my opinion if you want to visit places between Bruges and Normandy and prefer to drive. Know you have to cover large distances and can be boring. You can use the car to visit Damme north-east of Bruges and surrounding countryside and on the way south visiting Ypres is also worth to do. Further in France Arras and Amiens, the two V2 bases near Saint-Omers and other places mentioned. Driving along the coast Veurne still in Belgium has a little but nice main square, in France Boulogne-sur-Mer (still having it's medieval walls), Saint-Valery-sur-Somme, Étretat and Honfleur, places hard to reach with public transport. You can drop off in Caen or Rouen for going back to Paris for instance.

A car isn’t needed in Bruges, but it is helpful while traveling among the small towns in the Normandy area.

We had a trip some years ago, flew to Brussels, rented bicycles, took train to Bruges with them, then toured western Belgium by bike for 2 weeks. Returned the bikes, took train to Lille, then picked up a rental car for visiting Normandy and a bit of Brittany, plus chasing a bit of the Tour de France bike race.

You could take out the bike part, and go with trains and/or rental car. Price, location flexibility, schedules, and whether someone’s having to keep their eyes on the road, while someone navigates, might all factor into which is better. We returned our car in Caen, France, so it didn’t have to be returned at the exact same office where we picked it up. Some rental companies might charge more if you return a car to a different location within the same country, some don’t. Most will probably charge quite a bit, however, if you were to return the car in a different country than from where you got it.