Paris to Athens by train?

Looks like a very long train trip! Check out this site for some options: https://www.rome2rio.com/map/Paris/Athens

I have never done this trip but I know hat it isapproximately 50 hours of travel with multiple changes. You can plot out the journey at bahn.de. That will show you the travel time and the various train or ferry services from which you will need to purchase tickets. Good luck!

I’d suggest you consider flying instead.
This will give you more time in Paris!

Check skyscanner.net for flights.

If you do decide to go to Paris, after the Greece tour, make sure you book multi-city flights.
Fly to Athens and home from Paris.

You could go from Paris to Athens by train via Germany (Munich) or Switzerland (Zurich) then Serbia (Belgrade) and finally Thessaloniki then Athens.
Because of the connecting times between two trains you will probably need 3 days (or even 4).
Otherwise you could also go by train to Italy and take a ferry from a port in Italy.

It's the kind of trip that can be done by train fanatics who have a lot of free time

Trains in the eastern Balkans are generally very slow. I'm somewhat doubtful of their reliability. Huge fan iof trains though I am, I recommend flying unless you want to stop over in some of the fascinating places along the way. I spent a good bit of time traveling around the Balkans in 2015, much of that time on buses because of the limitations of the rail network.

The wonderful Seat61 website describes the route from London to Greece (via Paris) at this link:
https://www.seat61.com/Greece.htm

It takes 48 hours by train to Italy then ferry to Greece. Probably only worth it if you plan to visit Apulia on the way, before taking the ferry.

Thanks for all of the helpful advice!