Paris + Germany

Base on your description I think from Paris you could go to Strasbourg and Colmar (Alsace)
From there you can easily get to Germany or Switzerland taking the train
In Germany a lot of people go to Munich and tour the area around there known as Bavaria.
Google Bavaria or get one of the Best of Europe Guidebooks to start familiarizing yourself with that area
A guidebook would also give you other ideas.

In Switzerland you would want to go to the Berner Oberland area.
Same thing Google that and you will get some ideas.

Some general thoughts:

Before committing to any plan, look at Rome2Rio to get an idea of how hard or easy it will be to connect places: https://www.rome2rio.com/. Note that you should never use this site as the last word on schedules, fares, etc - go directly to the operator of the train, flight, bus, etc. But it's great for identifying snags that you weren't aware of.

Similarly, look at flight prices before finalizing an itinerary. For inexplicable reasons, a city can be cheap or expensive to fly to. For instance, looking for early October 2019, NYC to Madrid roundtrip on nonstop flights is $320 (not a typo), while Berlin is far more expensive for the same dates. You should never do something just because it's cheap, but it can be a great tiebreaker.

From Paris, you can take trains to parts of Germany, France, Switzerland, Belgium, the Netherlands, or Barcelona easily. For other destinations on a short trip, you'll most likely want to fly. To find train schedules, use the Bahn (German Rail) website following Rick's tutorial: https://www.ricksteves.com/travel-tips/transportation/trains/online-schedules

For flights within Europe, use Skyscanner: https://www.skyscanner.com/. Before committing, be sure to go to the website of the airline operating the flight, so you can learn about all the fees and rules (and there will be ones you hadn't anticipated, if you haven't flown in Europe recently).

If you're not taking a loop trip, be sure to book a multi city ticket rather than a conventional round trip (say, into Paris and out of Zurich or Munich). To find these, use the "multi city" or "multiple destinations" option on Kayak, Google Flights, airline websites, etc. Even if this is "more expensive" (and it may or may not be), you save time and money by not backtracking - very important on such a short trip.

If you want to see who flies where from an airport, look at that airport's Wikipedia page. Here's Paris Orly: https://en.wikipedia.org/wiki/Orly_Airport#Airlines_and_destinations and Paris Charles de Gaulle: https://en.wikipedia.org/wiki/Charles_de_Gaulle_Airport#Passenge . There's also Paris Beauvais, which mainly serves Ryanair, and is farther from Paris (so, allow more time and/or more money to reach it): https://en.wikipedia.org/wiki/Beauvais%E2%80%93Till%C3%A9_Airport#Airlines_and_destinations

You want to be in the city where your flight departs for the US, the night before your flight home. So, if you're not able to get a multi-city ticket, with only 10 days, you'll want to confine your trip to a small area, to make it easier to get back to Paris.

I'll just tell you what I'd do in your situation. In fact, I have done this before, though my kids were older.

I'd fly into Paris and spend several days there. Amazon has a few books on Paris for kids if you search for "Paris Kids".
A couple of places my kids liked were watching artists draw portraits outside Pompidou Museum, eating unlimited choc. mousse at Chez Janou, taking the Metro, top of Arc de Triomphe, street markets, revolving room at Cite de Sciences, playground at Tuileries: https://www.lesenfantsaparis.com/jardin-des-tuileries/.

From Paris, take the bullet train to either Geneva or Zurich, about 3 hrs. How to reserve that is at www.seat61.com

About another 3 hrs to Lauterbrunnen. There I would consider renting a trailer or bungalow because you will have your own kitchen. See www.campingjungfrau.swiss

Take to the trails, especially those with cows or sheep or goats. If you click on my name, you'll find a link where I list our dozen favorite hikes in the area, with pics and maps. You might consider getting the Berner Oberland Pass plus Family Card for kids so all the trains and cable cars in the area (plus all trains south of Bern or Lucerne) are covered.

https://www.regionalpass-berneroberland.ch/en/

You could reverse the procedure to return to Paris, or fly out of Geneva or Zurich.

Considering that there is so much to see in Paris, plus your first day or 2 maybe lost to jet lag, you could easily spend 5 days there. Does your 10 days include international travel?

With young children and at that time of year, when places will be busier, I would consider Paris plus one other base, otherwise you may feel as though you are spending too long in transit.

The Venise Verte (green Venice) in France would be a great base if you drove, staying in Coulon. This area is archetypal France - honey stone cottages with pastel coloured flowers and pale blue window shutters overlooking the extensive canal network (hence the reference to Venice). You could hire bicycles - the tracks are quiet and safe for children. It’s inland, so It won’t be as busy as the coast. La Rochelle on the coast is an hour’s drive away, with its fantastic food market, aquarium and day trips to the island of Re. The city of Nantes is another good day trip if you want cathedrals, museums etc.

I am hoping to return to this area in June.

Thanks everyone. You've got me thinking about whether we should go from Paris to the Jungfrau region of Switzerland and then fly out of Zurich, rather than go to Germany/Munich after our Paris stay. Any further thoughts on this? As mentioned, we'd be with our two little kids and this is in August. Price wise, it's about the same for us to fly home from Zurich as it is from Munich, so we could do either.

Hi,

My only experience traveling in Europe with kids has been with my grandson when he was 4, a month before his 5th birthday and again, two years later, a month prior to his turning 11 in 2011. There were four of us, we stayed in Paris and elsewhere in France. Six years later in 2011 he was over again with his mom in London, then I rendezvoused with them in Paris to go to Perpignan (5 hr TGV ride from Paris) changing to Collioure. Basically, we went separately and met up in Paris to start the next phase. Most of his exposure to traveling in Europe was in Paris and France using rental cars and trains.

I don't have children, but I think time in the mountains in Switzerland would be a great complement to time in Paris. However, if budget is of any concern, I suggest going to a website like booking.com and checking lodging prices in some places like Lauterbrunnen and Murren. Switzerland is not cheap--though I don't know what might be available at campgrounds.

The main issue here is budget. Lodging, transport, and food in Switzerland can approach double the cost of Germany. If money isn't a primary concern, Switzerland is more convenient via transport for a beautiful alpine experience, especially with your limited time.

If you are watching your budget, I'd suggest Alsace as another commenter already did. Easy TGV fast train from Paris to Strasbourg, and from there you can rent a car and spend several days exploring the beautiful villages. There are kid-friendly sights too, like "Monkey Mountain" where you can feed free-range monkeys and Haut-Koeningsberg castle. Colmar isn't a bad base (although you have many options) and if you want to say you went to Germany, it's an easy drive across the Rhine to Freiburg, a lovely university town in the Black Forest.

With such a short time, as much fun as Bavaria is for kids, I don't know if I'd want to make the trip all the way there.

I would spend a few days in Paris (3-4) and then consider the Mosel in Germany. You can go to Trier, which is on the border of France and Germany, and then go up and down the river. For the age of kids of yours, an agrotourismo might really be great - chickens, goats, etc. You can take boat rides on the Mosel. There are castles for the kids, and wine for you (assuming you drink). I'd do the train. Much easier with little ones. Plus bullet trains are incredibly fast.

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Hope it Helps.

"...then doing a week trip somewhere like into Germany...." Great! Easy... head north and east.

I would suggest choosing from these cities and towns, Berlin, Hamburg, Leipzig, Kiel, Lübeck, Goslar, Soest/Westf., Münster/Westf, Dresden, Meissen, Naumburg an der Saale, Weimar, Lüneburg, Potsdam, Eutin/Holstein. Bremen, Erfurt, .

I second Paris plus Berner Oberland. My kids LOVED it last year. Switzerland was the highlight of our trip. You can read a bit about it here (Switzerland is at the bottom below our cruise report). Also if you’re open to the idea a cruise is a fantastic way to take kids to Europe.