Travel from Chamonix to Paris.

When we took the My Way Alpine, we used Mountain Dropoffs, a shared van, to get to Geneva. You could also take a bus, but MD was reasonably priced and the times were better. They dropped us at the airport, and we took a train from the airport one stop to the main Geneva rail station. From there you can get a train to Paris and get to Gare de Lyon in 3 hours or so. That's probably faster than flying if you include security and getting from the airport to Paris proper. Enjoy the tour! We loved it.

I prefer train travel and you can do it this way - Leave from Chamonix on the Mont Blanc Express headed west to St Gervais Le Fayet and change there to The Leman Express L3 service which will take you to Geneva Cornavin ( Central Station ) TGV from there to Paris- further information - https://en.wikipedia.org/wiki/L%C3%A9man_Express Beautiful scenery assured !!

take a train from Paris to Annecy or Bellegarde (no need to go to Geneva I think) then public transport or taxi to Chamonix

There is indeed no need to go to Geneva. You just take the train down to St Gervais / le Fayet, where a regional train takes you to Bellegarde for the TGV to Paris. Total travel time 5:45, tickets sold on SNCF CONNECT.

When I have made this trip , I took the route via Bellegarde , but that was prior to the completion of the Leman Express . I would only add that depending on the scheduling of the trains , one of the two routings might be more convenient than the other .

As you can probably tell, you have multiple options. Kind of depends on your budget,
and how much you want to get there vs enjoying the ride.

The train to/from Chamonix has connections and can be slower since you're ascending/descending.
But the views are nice, if the train isn't crowded.

Bus service (Flixbus, Swisstours) is non-stop and can be faster but you have to get to Chamonix
Sud where the bus station is, and if you go to Geneva, there is a ~4 block walk between the bus
station and Cornavin train station (or go the airport and take the 7 minute ride, but you have
to buy a ticket). The bus is pretty inexpensive and comfortable, though. And as noted there are
plenty of shared van transfer options. Those may pick you up at your lodging in Chamonix.

You can train or bus it to Annecy (again, the train is slower but more scenic), then you could spend a
night (but not much more IMO) in Annecy before going on to Paris.

I did this route not long ago and the train was honestly the easiest option. You’ll usually need a connection (like via Geneva or Lyon), but the whole trip is pretty smooth.
The fastest options are around 5.5–6 hours, but realistically it can be a bit longer depending on connections.
One tip - give yourself some buffer time between trains, especially in winter. I almost missed a connection once because of a small delay in the mountain section.
Also worth noting: the first part of the journey through the Alps is actually really scenic, so try to sit on the window side if you can.
And small thing, but having mobile data the whole way made it much less stressful - I could track connections, check platforms, and adjust plans on the go instead of guessing.

Thank you everyone for your responses. From all this information I do believe we have a plan.