is it possible to take the TGV paris to stuttgart with a stop in reims?

This question is back to front. What you want to know is:

"I want to get from Paris to Reims (city centre), and then later in the same day from Reims to Stuttgart, is this possible?"

Whether the trains is a TGV or not is not relevant. You can look up train times on the DB website: https://www.bahn.com/en/view/index.shtml
Is the Champagne tour you want to go on starting in Reims? If not where?
It is about 1 hour from Paris to Reims (the station in the city centre), there are trains about once per hour.
For the second leg, there is a train at 17:05 which might fit (2 changes):

Reims dep 17:05 TER40808 Champagne-Ardenne arr 17:17
Champagne-Ardenne dep 17:35 TGV 5461 Strasbourg arr 19:05
Strasbourg dep 19:46 TGV 9579 Stuttgart Hbf arr 21:04

Reims and Epernay are two different towns in the Champagne area. The TGV trains direct from Paris to Reims terminate there and there are no direct TGV from Reims to Stuttgart.

There is a TGV station on the through line called Champagne-Ardennes that is linked to central Reims by both local trains and city streetcars. There are trains heading further east from Champagne-Ardennes, but not as far as Stuttgart - you'll have to change again. There is no official luggage storage at Champagne-Ardennes or the Reims city centre station.

It is much better done as a day trip from Paris. There is a direct TGV connection with Reims, taking 45 mins and as cheap as EUR 15 (single journey) when bought in advance.

You can go directly from Paris to Stuttgart in as little as 3 hr. 9 min. Traveling from Reims to Stuttgart will take much longer (at least 4 hr. 49 min.), so there's not really anything to be gained, timewise, by visiting Reims en route. It would, indeed, be easier to see Reims on a day-trip from Paris. I believe luggage storage is available at Paris's Gare de l'Est.

We did Paris/Reims last year and yes, it is 45 minutes by TGV from Paris and an easy day trip. I'd do that and then take the TGV straight to Stuttgart. In any case, it would be two trips and they wouldn't be 'on the way'.

Thank you, you have all been most helpful.
I have been looking at the trains and eventually worked out that I can take the direct train from Paris at 9:28am and arrive in Reims City Centre. at 10:15. Drop our luggage / hire a car? Fit in 1 tour of a Champagne house around 11am
We will then make our way back to the city centre and pick our luggage and catch the train to Stuttgart.
there is only a 1:17 or 5:43 train (doesn't seem to be anything in between, so I guess we will take the latter one)

I would like to go to Tattinger or Pommery with the family to tour the caves.
Which one do you think would be the most visually interesting? (I have 2 kids I will be taking to look at the cave (no tasting for them :) just mummy :)) so a short tour and look at the beautiful architecture before we hope back on the train and continue our journey.
Is it easy to catch a bus there? or should I hire a car?/ walk? I'm just a little nervous about missing the train connections.
kind regard
simone

catch the train to Stuttgart. there is only a 1:17 or 5:43 train (doesn't seem to be anything in between, so I guess we will take the latter one)

Simon, where are you looking for these trains? You should be looking at the DB website: https://www.bahn.de/p/view/index.shtml
For a random date in April next year I see:

Reims 14:15, 1 change, Stuttgart Hbf 19:04
Reims 15:15, 3 changes, Stuttgart Hbf 18:49
Reims 15:15, 2 changes, Stuttgart Hbf 19:04
Reims 17:06, 2 changes, Stuttgart Hbf 21:04
Reims 18:01, 4 changes, Stuttgart Hbf 22:58
Reims 18:01, 3 changes, Stuttgart Hbf 23:08

Some (but not all) of the above involve a change at Champagne-Ardenne , which is on the High Speed line outside Reims. If you are getting a hire car, consider getting it from there instead of Reims city centre.

P.S. "only a 1:17 or 5:43 train", I assume those are "PM", which is not used in Europe. Timetables always use the 24 hour clock.

P.P.S. Somebody suggested doing Reims as a day trip from Paris, and going direct from Paris to Stuttgart. That is a good idea.

Dear Chris
Thank you so much - you are a legend :)

If you are staying at a hotel, the hotel will be glad to keep your luggage. I don't know if the station is equipped with lockers.

You must reserve tickets in advance at Pommery. Tours are in English.

I think the Taittinger "crayeres" are the most interesting, but involve a lot of steps (impractical), which might be tiring for your children. I don't think strollers are permitted, so you will have to carry your children.
Tours are in English, as well as other languages. You should reserve at Taittinger, also.

Taittinger has elevators to the cellars for those for whom stairs are a challenge. I don't understand why you would rent a car to do this as Taittinger is a short bus ride from the train station or a not difficult walk. Having a car and the time it takes to rent one and return one and then try to park one would add a huge amount of time to the process. There is no quick pick up for rental cars in France as there is in the US.