Paris/Normandy/Belgium/Netherlands

Must you return to Paris? I think from some US origins a multi-city ticket into Paris and home from Amsterdam wouldn't be more expensive than a Paris roundtrip, and it would save you the cost and time of scurrying back to Paris on our last day.

You'll need at least 3 nights in Normandy for what you're describing. I'd prefer to keep this trip to France and one other country (actually, I've spent 4-1/2 months in France alone), but I guess it depends on what sort of tourist you are. Do you want to go inside a lot of museums and historical sights, or are you often satisfied with the exteriors? You'll lose at least half a day every time you relocate, so you could easily turn you 15 days into 11 or 12 by moving around a lot.

I think your plan to visit Paris, Normandy, MSM, (can be done by a Tour from Paris), Belgium and the Netherlands is doable in 15 days as these places are less than a days travel. Don't miss Chartres and Versailles...you can do these as Day Tours from Paris. Trains can be quicker, but driving allows for flexibility.
If you are planning 2021...things may already being booked up and prices are trending higher. Booking Land Tours that guarantee their prices might be a good idea. Be careful, because some book the accommodations with an additional cost.

I agree with acraven and that is to fly into Paris or Amsterdam and out the other.
While in Normandy, focus on Arromanches Port Winston Artificial Harbor (which wowed me more than Omaha Beach), Omaha Beach and the WWII Normandy American Cemetery and Memorial. You may also want to include Mont St-Michel to your itinerary.
In Belgium I would store my luggage at the train station in Brussels and visit Grand Place before moving on to Brugge where I would sleep. On your way to Amsterdam, you’ll have to change trains in Brussels so storing your luggage again while you visit the Royal Museums of Fine Arts of Belgium is a fine option.

Another vote for flying into Paris and home from Amsterdam, if that is still possible. Even if it were to cost you - hypothetically - $250 more, the time and aggravation you'd save would be well worth it.

Based on your plan, I would consider the following:
Paris 4 days (as you've already been there);

Caen 2 days - you can rent a car and do the D-Day beaches one day and MSM, the other; You can certainly do MSM in less than a day, and if so, you can spend the rest of the day exploring Caen: it's got a very good WWII Museum, a nice Museum of Arts, a great castle/chateau, a couple of cool abbeys, and some interesting churches.

Brussells, Brugges and Ghent 5 days total - they're all relatively close to one another via train, with frequent trains running throughout the day (Ghent is beautiful and can be accomplished in one full day). And all three are very walkable and have lots of inexpensive bike rentals available;

Amsterdam and surrounding cities 4 days total. I've only been to Amsterdam so I can't offer any advice on any other Dutch cities.

Best of luck

If you do go to Amsterdam, try staying in nearby Haarlem. Visit Amsterdam during the day to do your sightseeing, then take the short train ride back and forth to Haarlem to spend the evening and sleep. It's a beautiful city in itself and feels much safer and more relaxed in the evening than Amsterdam.

Also, for Normandy area, consider taking the train from Paris to Bayeux, then renting a car there. That puts you very close to the DDay sights, and don't miss the Bayeux tapestry! Bayeux is a nice, medium sized town with good hotels and B&Bs and is fairly easy to navigate. You can go to Caen from there to see the excellent WWII museum, bu I would stay in Bayeux because it's closer to the beaches

Just an idea: if you spend 3 days in Belgium and 3 in the Netherlands you can spend 9 in France.
Jetlagged arriving in Paris take as already noted the train to Caen or Bayeux, rent a car there to explore Normandy. Heading north to Belgium you can drop off the car in Lille for instance and visit the Cathedral of Amiens, the centre of Arras and Lille is worth a visit too. From the latter easy trainride to Ghent and use it as a base for trips to Bruges and Brussels. On the way to the Netherlands you can visit Antwerp, there are luggage lockers at the train station.

After Normandy another option is visiting Giverny on the way to Paris. Instead of dropping off there you can drive further along the Seine to La Roche-Guyon, through the Vexin region to van Gogh’s Auvers-sur-Oise. Following the N104 you can go to CDG for taking the TGV to Brussels or keep the car for a visit to Chantilly, Senlis and Lille. PM me if you want further details.

I think Wil has a great suggestion and I have nothing to add to it.

And you really should fly open jaw. If you live in New Jersey it is not hard to book an open jaw with non stop flights to Paris and home from Amsterdam.

TY All for the responses. All good stuff to take in consideration.

You didn't give your self-guiding skills/desire or energy level. I just want to observe that you have picked a large amount of ground to cover, and ambitious local action at each (presumed) sleeping point. For example, Normandy is quite far from Belgium, especially Wallonia. And (I have personally been to Brussels as a daytrip from Antwerp at least four times, in four different years) even an easy local situation can become tedious when you have to go the train station every morning and wait in line to buy a ticket for the day. MSM is a time consuming project from Caen or Bayeux. You don't just jump on a train.

You should use the search box here to read each of the many opinions of which city you should sleep in for Belgium! If I had only a few days sleeping in the Netherlands, I would content my self with sleeping in Amsterdam (not Haarlem) and visit (by commuter train) places like Den Haag, Delft, Leiden, Utrecht, and maybe Amersfoort or Alkmaar. So I'd skip the eastern part of the Netherlands. Weather and daylight hours may not be as good in October as summer. I hope the reduced crowds compensate for this.

Don't forget the need to plan for Monday closures. Just one example, (pre Covid, anyway) the Mystic Lamb (assuming it's all back together yet) in Gent is open seven days, although the other places in town may not be open Monday. But it's a nice place to walk around, even with closures.

We do a lot of day trips into Belgium by either car or train. Of the cities mentioned, we prefer Ghent to Bruges, and Antwerp to Brussels. Ghent is far less touristy than Bruges; it's an incredibly historic city and the college crowd keeps it young. Antwerp is our go-to place, much more intimate and relaxed than Brussels. We often train down to Antwerp for lunch - my wife window shops the diamond district (ever-hopeful), and we hop back on the train.

Tim touches on many of the great cities & towns in the NL... buy an OV-chipkaart and hop on and off the trains! Haarlem, Den Haag, Delft, , Utrecht, Amersfoort, Hoorn, Alkmaar, Naarden, and Lisse (for Tulips)are within a hour of Amsterdam - even Rotterdam is not much farther. And don't forget to give yourself time to BIKE in South & North Holland!

I too like the open jaw into CDG and home from AMS.