After some brainstorming, (I thinked it for a few seconds) I decided to sand them and not re-varnish the set.
Restoration of an old chess set. (Chavet n°3)

A few hours later, the first chess pieces were finished.
And some days later, it was done. Take a look on this pawn at the midle. Il like so much this Jura wood.
Here the white Queen. Isn't it cool?
The complete set:
What do you think about it?

They look very nice although I'm inclined to maybe have 2 small points (from a amateur point of view, I have no experience at all at attempting to restore wooden pieces):
1) the lines on the knights face are a bit soft now instead of the crisp lines which you still have on the black pieces
2) if you don't seal the wood in some way, the sanded white pieces will be very prone to accumulate dirt and skin grease which will stain it at the spots where you touch the pieces while playing so maybe that's something to consider

Bravo! I much like the result. It will be a pleasure for you to play with.
I agree a clear wood sealer is a good idea (in French language: "bouche-pores" ou "fond dur").
Cheers!

They look very nice although I'm inclined to maybe have 2 small points (from a amateur point of view, I have no experience at all at attempting to restore wooden pieces):
1) the lines on the knights face are a bit soft now instead of the crisp lines which you still have on the black pieces
2) if you don't seal the wood in some way, the sanded white pieces will be very prone to accumulate dirt and skin grease which will stain it at the spots where you touch the pieces while playing so maybe that's something to consider
Thank's for your constructive comment. Yes it is right, lines are a little bit softer on white Knights! I think the next time it will be better, pehaps I may use a Dremel.
For the second point, i was thinking the wax was enough to protect the wood from dirt. But maybe i'm wrong?

Sorry, waxing them would be enough. Since you didn't state that you did so I wrongfully presumed you hadn't. 👍
Nice work, I would be thrilled to own the set!

Thank's! You are absolutely right, i forgot to mention this point. I'm sorry. So yes of course, i waxed and polished each piece. Otherwise the parts would not have this rendering. I used a wax i made myself, and also some bees helped me! ^^ So some beeswax with essence of turpentine (cire d'abeille et essence de thérébentine, in french)
And thank's to all for your feedbacks, it's apreciated! :-)

Great effort, you brought them to a new life! Great setting with red table, leather board and garden, too!

thank's! Yes i will redo the felt, there is a need. Next step!
Hello to everybody.
Recently I bought this old "Jeux Morize" chess set whose pieces were made by Chavet. It's a n°3 size.
The varnish was cracked and also the "white" ones of an horrible colour, as if it had undergone passive smoking for a while.
As you can see it was in bad condition, but complete. And nothing impossible to repair.