First trip to France: need help filling a gap in my itinerary

How about Dijon? Direct train from Lyon in 2 hours or less. Easy day trip (or additional trip) to Beaune.

To throw out a few suggestions:
Trip to Besançon - if you are interested in WW2 history there is a Vauban fort which was used as SS HQ and has a fascinating, if sombre, museum.
Mulhouse, which has the national railway and motor car museums.

Consider Alsace. There are both direct TGV trains as well as less expensive connecting service between Lyon, Colmar/Strasbourg and Paris.

If you base in Colmar you can easily visit the wine villages by train, bus, Kutzig Bus, bikes or walking as well as several other places. You'll get beer, wine, traditional Alsatian food, museums, architecture, WWII, wineries, nature and more. With a bit of work you'll also find WWI sites and Roman connections.

I am with jeanm. Alsace will give you a great week!

Alsace is good. And kudos for figuring out to END in Paris rather than having to waste a good travel day getting back the day before the flight.

Another good option is to add the time to Paris or half the time to Paris. Paris is a great place for day tripping in addition to what it has to offer. You could do the Champagne houses of Reims, Monet's garden at Giverny, Rouen, Amiens, Auvers sur Oise where Van Gogh lived his final days. There are numerous interesting chateaux all easily within an hour or two of Paris by train. It is a great location if you don't have a car. There is a book by Simms that details 20 less well known day trips within an hour of Paris. You have left barely time to see the highlights of Paris -- adding the time back there and doing some regional day tripping would be great.

Lyon is a center of both Roman and WWII history, as well as a culinary capital, so you might want to spend more time there. Just south of Lyon is Vienne, a major Roman seaport with many ruins and an excellent Roman museum across the Rhône. This is also part of the Côte du Rhône wine region.
Next, you could go north taking a few days via Dijon and Beaune in Burgundy for medieval architecture, cuisine, wine and art.
Finally, if art, architecture and cultural landmarks are priorities, you need to add more time in Paris where all is present. From Paris take a day trip to Fontainebleau, not only to see the chateau but also to also hike in the huge forest, formerly the king's domaine but open to the people since the Revolution.

We stayed in Vienne once randomly -- we were driving from Alsace to visit friends in Provence and it was sort of half way. We were thrilled with the place filled with archeological digs and old Roman ruins. One of those lucky happenstance of travel and stumbling on something good. We picked it for location and because it was small as an overnight stop is always logistically difficult in a larger city.

Hi,
I'd go south by train to Avignon, Arles, and Nimes (or Aix en Provence). You'll see roman ruins, medieval history, art, architecture, cultural land marks and great food wine and beer. You could stay in Avignon and do day trips or stay 3 nights in one city and 3 in another.
You can take a bus or a rent a car at the Avignon station and see the Pont du Gard. Maybe even rent a canoe and paddle under the Pont.

The problem is, in all 4 locations, I suspect there will be tourists due to the season (no matter where you in June that will happen).

I think with no car Alsace may be harder to get around, but I'm sure you could do Lyon for 2 nights and see the ruins/eat/drink/MFA there, then hit Orange for the roman theatre, then head north to Dijon and Beaune for short stays for some more great food, wine, history, etc.

Good luck what ever you choose

You should plan on visiting a lot of supermarkets to buy food there. So much good food in France!! Have fun exploring the markets - wine is very reasonable, there are often 12 varieties of pate and many varieties of baguettes and other breads.

In Paris, consider the Boullion restaurants, where you can get a 3 course menu for 15 E. Long waiting line - don't go at 8 PM. We went 2x to Boullion Chartier in Montparnasse. Also there are "restaurants ouvrier" or workingmen's restaurants - full meal at noon including wine or cidre for 16E.

As to the June 24-30 period, pull up a map of France, find Lyon and Paris and look between them. One option is to take a short train ride to another large city for a day or 2, again to another, and end in Paris. Look for hostels - you can get a separate room for a modest sum in many.

An overnight trip you might enjoy would be to take a train to Le Puy-en-Velay. It's in a volcanic region and is very hilly with structures and statues situated at seemingly impossible locations. Lots of stair climbing that is well-rewarded with views and cultural sights.

Don't miss the Gallo-Roman museum in Lyon, the ampitheatres, and Vienne. The Resistance and Deportation museum in Lyon is quite good. And the Musée des Beaux Artes in Lyon is definitely worth a stop. Even if you don't go in the museum, the shaded garden in front behind the walls provides a pleasant place to relax after seeing la Fontaine Bartholdi in Place Terreaux (which the museum also fronts). It's a terrific fountain sculpted by the fellow who did the outside of the Statue of Liberty (Eiffel, of the tower fame, did the inside structure of Lady Liberty).

I agree with Bob that Le Puy-en-Veley will knock you for a spin, and it is off the American tourist route. But bring a sweater as it's at higher altitude and can be chilly even in summer.

We like:
History, especially Roman and medieval history, World War I and II, cinema

Lyon has two museums that you may find interesting, Musée Cinéma et Miniature and Musée Lumière

You have many great choices:
1)Colmar/Strasbourg the Alsace Region of France
2) Geneva and more in Switzerland -Great, but Switzerland is one of the most expensive countries in Europe,
3) Take the train down the Rhone River, visiting historical places- River cruises usually go from Lyon down to Arles. You could take the train and stop in several cities along the Rhone. Cities like Vienne, Avignon and Arles.

https://www.french-waterways.com/top-landmarks-monuments-river-rhone/
Arles is close to the French Rivera and you could visit Nice, Cannes and Monaco.
4) Carcassonne and the Bordeaux region in SW France- It's great but with more travel.