Logistics of travelling between 4 countries in Europe

I would not double back to the starting point. You will usually save time and money with a "Multi-City" flight itinerary for your trans-Atlantic route, whether that's into Dublin and home from Munich or into London and home from Dublin. London to Paris (or Brussels) is faster by train. The best-timed flight connection from Munich to home might actually be in Frankfurt, Amsterdam, or elsewhere.

I frankly think that some of these destinations are not worth a big effort for a short visit when you don't have time to see more along the way. Mont-Saint-Michel and Carcassonne particularly fit that bill and I would skip them. London and Bath are actually easy to reach, but that means that you could include them on almost any other future trip to Europe. If you skipped those, then you might have time to add the Dordogne in between MSM and Carcassonne.

Beyond what you've already seen in France and Germany, there must be other attractive destinations that would fit a more natural route. You could also consider Belgium or the Netherlands, instead of France.

See www.skyscanner.com for budget flights within Europe. Looking Up Train Schedules and Routes Online gives you the Deutsche Bahn train schedule link and tips for using it.

FYI, there are nonstop flights from Toulouse airport (nearest to Carcassonne) to Frankfurt, Hamburg, or Berlin, but not Munich.

GERMANY: drive? train? fly? from Carcassonne, ending up near Nuremburg for 3 days, then flying back to London/ Dublin for the flight home, probably from Munich

Travelling by train from Carcasonne to Ansbach is a 12+ hours trip involving a transfer from the Gare de Lyon to the Gare de l' Est in Paris. I'd rather look for flights (there is a daily non stop Lufthansa flight from Marseille to Frankfurt). Trainwise, there is not much difference between going to MUC or FRA from Ansbach.

Public transport in the Ansbach area is good. It belongs to the VGN (Greater Nuremberg Area transport authority) and you could do daytrips from Ansbach as far as Bamberg on a cheap VGN day pass.

My thoughts are the same as Laura's. The last thing I'd want to do on a vacation is head to an airport every 2-4 days. There are many interesting destinations in Brittany and Normandy that could be coupled with Mont St Michel, and nearly uncountable wonderful options in southern France not far from Carcassonne. There are inexpensive tours to the Cotswolds offered from Bath, and Wells and Salisbury are also rather close.

For me, trying to get to all the areas you mentioned in three weeks would be miserable.

Lots of very cheap air flights from Dublin to Bristol (check Skyscanner). Frequent, 50-minute bus transport from the airport to Bath. https://www.bristolairport.co.uk/to-and-from-the-airport/bus-and-coach
Then train or bus to London, as desired. Much easier using Bristol airport than any London airport.

The French leg of your trip will be arduous. The trip to Mont St Michel will take most of the day, as will the drive to Carcassonne.

May I suggest that there are sights of equal or greater charm and quality that would be logistically less of a challenge? That is ultimately a personal decision of course, but you could spend all four nights in Normandy, or in the Perigord, without feeling bored.

Second on the Bristol front. You're wasting time flying to London, taking a bus/train to Bath and then return to London when it's easier and cheaper to fly to Bristol, visit Bath and then move on to London.

Thanks for all the great info. I appreciate everyone's tips and suggestions. You have all given me several good ideas that will help me plan. Adding a few days here or there is not a problem. I will try to pace myself slower. Multiple flights are not ideal, but will cover a lot of ground quickly.
France is my favorite country and I missed the entire Normandy area last time. Adding that to the Mont-Saint-Michel stop for sure.
I've driven thru the Dordogne area before on my way to Lascaux II, but would like to see La Roque-Gageac & Beynac-et-Cazerac this trip. I've still gotta see Carcassonne, so I'm now thinking about making Toulouse a central base, renting a car and taking a couple of day trips.
New thoughts:
ENGLAND: Flight from Dublin to Bristol, Bus to Bath, Train to London. From London- train to Calais. Rent a car in Calais.
FRANCE: Drive to Normandy area, stay a few days. Fly out of Rennes to Toulouse. Rent a car and drive up toward Montignac area and back past Toulouse to Carcassonne. Shorter day trips.
GERMANY: I'll look at flying out of Toulouse to Frankfurt/Munich. Train from Frankfurt/Munich to Ansbach or Nuremburg if necessary. Flight back to Dublin from Frankfurt.

It is still a lot to do in one trip, but this is probably my last trip to Europe. I've been using rometorio.com for transportation ideas/options. Thanks for the links to plane/train schedule sites, etc. I always love to hear and see ideas and travel tips, so feel free to add your thoughts. Thanks again. Bon voyage ya'll.

From London- train to Calais. Rent a car in Calais.

Make that Lille. Very few trains from London stop at Calais (Calais-Fréthun), the station is in a field well outside Calais. Many trains stop at Lille, it is a much bigger place with many car hire opportunities.

Train from Frankfurt/Munich to Ansbach or Nuremburg if necessary.

There is a S-Bahn every 30 min from Nürnberg to Ansbach and an hourly connection from Frankfurt with one transfer in Würzburg. Travel time from Munich Airport and Frankfurt Airport is more or less the same (approx. 2:45), but Frankfurt is easier since it implies just one transfer (in Würzburg, as said) while Munich implies two, Munich Hbf and Nürnberg Hbf.

Are you returning to Dublin to continue to tour Ireland on the back end, or are you doing your Ireland tour at the start before going to England? Why don't you just fly into Dublin and out of Munich or Frankfurt, or vice versa? No need to return to where you started.

Thanks for the Lille train info and the German train info.
To answer the question...I'm flying into Dublin and will begin my trip there on the front end. I can't handle the longer flights health wise, such as from Frankfurt to US. So, yes I'll be returning to either London or Dublin at the end to fly back to the East Coast. It's easier on me to break the trip up into shorter flights, even though it's inconvenient. Thanks again everyone.

I'm glad to hear that you can add more time. That's always my preferred solution.

I don't see how you can see what you want to in Ireland with only 2-3 days there. You've mentioned day trips from two different cities but you have to arrive and get between the two cities as well. Not to mention departing for London. I think you need more time there, or to reduce your geographical targets.

The idea of train to Lille is pretty good, but you're still quite far there from Mont St Michel (300-400 miles). Via Michelin estimates 5.5 hours' driving time, but usually you should add to that to get a realistic time. (Plus picking up the rental car, etc.).

Basically every single element of your trip is terribly far from the others, especially within France. And with only three weeks for the whole trip ( a bit more, now, I understand), it would take you that long alone to see Normandy, Dordogne, and Carcassonne without rushing around -- much less adding on Ireland, England, and Germany!!!!!!! I'm sorry to be a negative Nelly, but this trip doesn't sound realistic to me at all.