Car or train for this itinerary?

Do I need a car for Amboise and/or Beaune?

It depends on what you want to see and do. But in general I'd say no.

I want to go to Chateau Clos Luce, is it doable by train?

It is in the town, so no you can't get there by train. But if you are staying in Amboise it is probably walking distance to Chateau Clos Luce.

So, can I wait until I get to Colmar to rent a car, taking the train
from Amboise to Beaune to Colmar, or is it better to drive from
Amboise to Beaune to Colmar?

Yes you can. Amboise to Beaune requires going through Paris, but is perfectly doable. Beaune to Colmar is very easy, 2:20 with direct TGV.

I‘d get a car for Amboise if you plan on visiting many chateau

You don't need a car to visit Chateau Clos Luce if you're staying in central Amboise because it's within walking distance. If you want to venture out to other nearby chateaux a car will be helpful. Maybe rent a car for a day while you're there? Having a car to visit the towns on the route du vin near Colmar is a huge plus. Once again, you could rent for the days you need it because you'll probably also be spending time in Colmar itself. I haven't been to Beaune. Hope this helps.

I know that it is your first time in France and that it could be stressful, but I would get a car for the whole trip from Amboise (take train to Tours, rent in Tours), drive to Beaune, drive to Colmar, and drop the car off either in Colmar or in Strasbourg after your visit.
Amboise-Beaune is <4 hours and Beaune-Colmar is <3 hours, on good and generally rather quiet highways.
Whereas Amboise-Beaune by train is cumbersome, with the need to cross part of Paris by taxi or public transport, and several changes. Beaune to Colmar by train is OK (I was surprised to see that there is even a direct connection!) but a car will provide more flexibility and very little hassle.
And yes, the car, while not essential, will be useful in both Amboise & Beaune.

Thanks, all! I didn't realize Chateau Clos Luce was so close. Renting a car for one day, then again in Colmar, is a good idea. I was trying to avoid having a car for most of my trip.

Balso, I didn't know that. Thanks.

I did the exact trip that Balso described, in reverse. Picked up a car for Alsace, drove to Burgundy, drove to Loire/Amboise and returned the car to Tours and took the train back to Paris. IF, you are comfortable driving in France, then, yes, a car would be best for your journey. If you are not comfortable, you can see what you want by train/bus/bike/walk

From Paris CDG airport you can take a train to St-Pierre-des-Corps (2h 15m) where you’ll need to transfer to get to Amboise (St-Pierre) station (15-minutes). If you rent a car, you can do so at the St-Pierre-des-Corps train station and drive to Amboise (30-minutes).
When I was in Amboise, I took a bus to Chenonceaux. What’s tricky about taking the bus is not knowing what side of the street to catch it so ask your hotelier or Airbnb host.
Another note is I ate the best French onion soup at Restaurant Anne de Bretagne. It was the broth that made it delicious.
The train from Amboise to Beaune will take a full day that involves arriving at the Paris Austerlitz station on the Left Bank and crossing the River Seine to get to the Paris Gare de Lyon station (15-minute walk). Total time takes 7h 45m. If you drive from Amboise to Beaune, it will take 4h. There is a direct train from Beaune (Chagny) station to Colmar (2h 30m). If you drive it will take 2h 45m. The train between Beaune (Chagny) station to the Dijon Ville station takes 30-minutes.
To get back to Paris there’s a direct train taking 2h 45m but it’s departs around 5:30p.

The train from Amboise to Beaune will take a full day that involves
arriving at the Paris Austerlitz station on the Left Bank and crossing
the River Seine to get to the Paris Gare de Lyon station (15-minute
walk). Total time takes 7h 45m.

There are faster connections as well, I see one that takes 5:18. Including plenty of time to walk between the stations in Paris.

If you drive from Amboise to Beaune, it will take 4h.

That is a very optimistic driving time between Amboise and Beaune.

There are faster connections as well, I see one that takes 5:18.

How many connections does that train have? The one I suggest has one. However, I checked the schedule again and see one from Amboise to Beaune taking 7h 30m. Transfers at smaller train stations can be a hassle if you're hauling around luggage and you need to climb stairs.

That is a very optimistic driving time between Amboise and Beaune.

https://www.viamichelin.com/web/Routes?departure=37400%20Amboise%2C%20Centre-Val%20de%20Loire%2C%20France&departureTid=city-1364189&arrival=21200%20Beaune%2C%20Burgundy-Franche-Comte%2C%20France&arrivalTid=city-1313158&index=0&vehicle=0&type=0&distance=km&currency=EUR&highway=false&toll=false&vignette=false&orc=false&crossing=true&caravan=false&shouldUseTraffic=false&withBreaks=false&break_frequency=7200&coffee_duration=1200&lunch_duration=3600&diner_duration=3600&night_duration=32400&car=hatchback&fuel=petrol&fuelCost=1.451&allowance=0&corridor=&departureDate=&arrivalDate=&fuelConsumption=6.8:5.6:5.6&shouldUseNewEngine=false

How many connections does that train have?

Two, one in Paris and one in Montbard. And I doubt there will be any need to climb stairs in Montbard. It is a small station, so the two trains will probably use the same platform.

And Viamichelin are not as optimistic about driving times as Google maps, but they are still on the optimistic part of the spectrum.

Hello from Wisconsin,

Normally I would say, get a car. But that was when rentals were $20/day or less. Last I checked they are double or triple that rate. And availability may be an issue. With a car, parking where you are planning to stay can be a concern. Some hotels offer a spot for an extra charge..

You might rent for 10 days. A train out to your first stop and then rent the car, dropping it off at your last non-Paris stop and train it back into the city of light. (or is that Budapest?)

wayn eiNWI