Paris day trip and overnight trip advice

I’m currently spending 3 nights in Colmar and it has a very different feel from Paris (or Normandie or Loire Valley). It is quite busy, though, so it might not meet your criteria of non-touristy although right now most visitors seem to be German-speaking.

It was an extremely easy TGV train ride of ~2 hours with no changes.

Editing my answer to say the train journey is actually 2.5 hours. Currently on the return train to Paris with good wifi. The train out and back was/is full.

The town of Troyes is very picturesque (lots of half-timbered buildings tilting at crazy angles) and seems only rarely visited by non-French tourists. The train trip is by TER, so no advantage to pre-booking. The trip takes just over 1-1/2 hours from Paris Est. I have no idea how convenient the latter station is to your place in the Marais.

I've read good things (including on this forum) about Le Mans but haven't been there yet. It's a definite for the next time I go to France. Le Mans is most efficiently reached by TGV, so that's a potential cost issue if you want to be able to make a spur-of-the moment decision. The fastest trains take about an hour and depart from Paris Montparnasse.

How about Brussels? It is about 1 1/2 hrs. via train.

I would suggest going to northern France, ie to Amiens on the Somme and seeing the towns in that area.

My other suggestion is also Troyes, dep. from Gare de l"Est.

Stay the night, with a rental car you can proceed to the town of Brienne, where the big Napoleon Museum is located. It was established recently in the same building where the young Napoleon spent his military school years. Brienne was the first place where in 1814 Napoleon encountered the invading Allies, this time a combined Russian-Prussian force , they lost.

Lyon might be your style. It’s an easy enough train ride. I did an overnight there and enjoyed it quite a bit. It’s a big city, but cleaner and lacking the hustle-bustle. It’s like a genteel Paris. The old town is cool to wander around, and there are fantastic restaurants everywhere.

Colmar & Chartes are a good overnight. Chartes has a light show in the evening at the Cathedral & around it.

https://www.chartresenlumieres.com/en/

There are tons of places much closer to Paris than all of these; some here.
https://janettravels.wordpress.com/category/day-trips-from-paris/
For overnight trips, some we have done include: Lyon, Nantes, St. Malo, Bayeux -- there are many. Most that require an overnight would benefit from at least two nights which gives one full day.

zero interest in Versailles or other opulent places - not our thing Giverny is on our radar but is there better gardens nearby? My wife is keen to see natural style gardens vs super formed ones like Villandry

Have you been to Versailles? The gardens are so big that it is fair to say there are some more natural sections, and azalea groves and arboretum fragments. Parc Balbi is apparently walkable, but I've never been there.

Without a car you will be hard pressed to visit destination gardens, which are often remnants of palaces and estates. I haven't been to Chateau Chantilly, but that might have a garden. Have you seen Paris' version of The High Line, and the Parc Floral de Vincennes?

I recommend French Gardens, A Guide by Barbara Abbs, ISBN 0-89831-041-5. She says, "Courances is probably the most beautiful formal garden in France." Malmaison is on the RER. Sceaux sounds good but maybe not public transit. Fontainebleau should have enough tourist infrastructure to get transport or a private guide.

Find the book, "An Hour From Paris" by Annabel Sims.

http://anhourfromparis.com/

Domaine de Villarceaux, some 20km east of Giverny is really lovely. It’s more a park, I visited it in April 2018 during the week and there were just a handful of visitors. Entrance was free and think / hope still is. https://villarceaux.iledefrance.fr/

Further some 30km southwest of Versailles Les Vaux de Cernay, ruins of an abbey with hotel and restaurant in a stunning setting. Hotel seems temporarily closed, no idea why and for how long.

But….for both places you need a car.

The historic centre of Le Mans as already mentioned is much overlooked but certainly worth a visit. You can combine it with a visit to Chartres, there are direct trains between the two. Train from Chartres to Montparnasse in Paris stops in Rambouillet and Maintenon. The latter has a very lovely château with garden and park, not exactly you are looking for neverhteless a charming place worth to consider to my opinion.