I really liked Strasbourg. France meets Germany in a compact historical center, 2hrs each way from Paris on the TGV. Just go when the EU government is not meeting there, because for 4 days a month, they all have to pack up from Brussels and move to Strasbourg. Reims and the Champagne region are on the TGV to Strasbourg as well, making that an easy day trip from Paris.
There are also the night trains (Intercities de Nuit), which go from Paris to some destinations at the periphery of France that are way too long for a normal day trip. It is usually 4 or 6 bunks in a room, but you can pay extra to book the entire room for the two of you. Go to sleep in Paris and wake up 12 hours later in Nice on the Med coast, Briancon (ski resort town in the Alps, great in Summer too), or any of the medieval towns in the Pyrenees near Spain (Carcassonne, Narbonne, Perpignan)
Thanks for the Strasbourg tip. That's one of the places I was looking at based on the map. The German cultural influence drew me in. Thanks to your comment I checked the EU schedule and found they will be in Strasbourg at the same time.
I like the idea of a night train, but there is a significant chance either my wife or I won't be able to sleep. That would make the next day unpleasant, so we'll save the night train for some time when we have a few more days to spare.
There are also the night trains (Intercities de Nuit), which go from Paris to some destinations at the periphery of France that are way too long for a normal day trip. It is usually 4 or 6 bunks in a room, but you can pay extra to book the entire room for the two of you. Go to sleep in Paris and wake up 12 hours later in Nice on the Med coast, Briancon (ski resort town in the Alps, great in Summer too), or any of the medieval towns in the Pyrenees near Spain (Carcassonne, Narbonne, Perpignan)