Paris to Barcelona October of 2023

Rick Steves has a new FR guide book coming out in the fall of ’22 (20th edition). I would take his self-guided walking tours of Paris so you don’t miss seeing anything. Plan on one full day for each walk.
You also want to visit the Orsay Museum. Make sure you do that first thing in the morning when you have the most energy. I would buy tickets online before leaving home so you don’t have to wait in a long line (although it does move fairly fast).
I also recommend taking this tour one evening: https://2cvparistour.com/.
From Paris take a train to Beaune (2h 15m) that requires a transfer. Pack light and do laundry often. When traveling via public transportation it’s not uncommon to have to hull bags up and down stairs. Beaune makes a good base to explore the Burgundy region and appreciate some of the best pinot noirs you’ll ever taste. Rick Steves guidebook will tell you how to get around.
From Beaune take a train to Annecy (4h and requires a change) and sleep there for two nights. From Annecy take a direct bus to Chamonix and explore the French Alps.
From Chamonix you can take a direct bus to the Geneva airport (2h) and fly nonstop to Barcelona for less than $50 on Easyjet. The further out you buy your ticket the cheaper it is.
In Barcelona you want to visit the Picasso Museum and the Sagrada Familia (buy tickets online when you purchase your Orsay Museum tickets). That line is a block long if not longer and does not look like it moves fast.
Rick Steves next Barcelona book (6th edition) also comes out in another year. I recommend taking his self-guided walking tours in Barcelona too so you see it all. Barcelona is my favorite city in Spain. You also want to take day trips to see Salvador Dali’s Theatre-Museum (buy tickets before leaving home) and Montserrat.

What sort of things are you interested in seeing and doing? Are you a pair of adults, or does your travel party include children?

I find Barcelona fascinating and worth more than a week unless you are inclined to avoid all museums. Even then, if you're nuts for Catalan modernism like I am, you could probably fill a week just tracking down all the great buildings. There are other significant points of interest in Catalunya, including Girona and the Dali Theatre-Museum in Figueres. I haven't been to Montserrat, but it's a popular day trip. The Pyrenees would be easiest if you wanted to rent a car for at least a few days.

There's extremely rapid train service from Barcelona to Madrid by way of the interesting city of Zaragoza, so it's easy to add time in Zaragoza and Madrid once you're in Barcelona. Although I don't find Madrid as visually appealing as many other cities in Spain, it has some magnificent art museums and lively nightlife. And it may have the best set of day-trip options in Europe, Toledo, Segovia, Salamanca, Cuenca and Alcala de Henares being my favorites. Depending on your interests, some or all of those would be worth a one-, two- or three-night stay.

Or you could combine Barcelona with one or more stops in Andalucia if you're fans of Moorish architecture. You could fly or spend not that much extra time and go by train. The three major cities in the south are Seville, Cordoba and Granada.

Spain is a large country with important sightseeing destinations scattered all over. It would take many months to see just the major highlights, so it all comes down to what you prioritize. I'd tend to want to see a bit more than Catalunya with the amount of time you have.

As already pointed out, there are tons of great destinations on the French side of the border between Paris and Barcelona, too.

One thing that's worth thinking about is the big-picture question of whether you'd rather focus primarily on large cities and not move around very much or change hotels more often and experience quite a few smaller places.

We like to combine a European land trip with a transatlantic cruise back to the USA to avoid flying and enjoy a cruise.

If you have 3 to 4 weeks of travel from Paris to Barcelona, I would not extend the trip into southern Spain, it adds more travel and you can come back and do southern Spain as well as the Madrid area.

There is a lot to see between Paris and Barcelona.
You have some options;

1) The eastern route would take you to Lyon and down the Rhone River valley through Provence and SE France. Take the high speed train to Lyon, and rent a car (we did a river cruise, but that is more expensive) and visit Provence and the French Riveria, then take the train to Barcelona. You should plan on a week in Barcelona. Don't miss Monserratt and Girona.
2) The western route would take you through the Loire Valley for 3 nights, stay in Tours or Blois and visit some amazing Chateux. Then head down to Bordeaux for a week, enjoy some great wineries. After that you can visit the Basque region of northern Spain (Bilbao and San Sebastian) for 4-5 days, then on to Barcelona.
3) Other choices would be exploring Normandy instead of the Loire Valley on the western route or Straussbourg and Alsace on the eastern instead of the Riveria.

You can take a direct train from the Paris Est station to Colmar (2h 30m) that’s located in the Alsace region if you’re a white wine drinker. You can also rent a car in Colmar and drop it off in Annecy.
If you prefer taking public transportation to get around there is a train from Colmar to Beaune but does require a transfer (2h 45m).

Your 21-day BOE tour (Amsterdam to Paris) will have taken you to Beaune and the Swiss Alps, so you may not want to revisit those areas unless you know you'll want to see more than the tour provides. I'd certainly suggest spending some of your post-tour time in Paris. A week would be enough for a good taste of that city and some day trips like Versailles or Chartres or wherever. Then my own suggestion would be a couple of weeks with a car making your way south -- the Loire, the Dordogne, and Provence would all be good destinations, but I wouldn't suggest all three. Research some guidebooks to see what interests you most. "Wine country" would cover most of France, certainly those three regions (but not Normandy or Brittany).
Return the car in a city in southern France with good train service to Barcelona. (Returning it in Spain will mean a big drop-off fee that you don't need.) Then spend about a week in Barcelona and environs before your cruise.

A week in Amsterdam, three on the tour, four more before the cruise, and maybe ten days for the crossing = 9+ weeks total. I'm green with envy! ;-)