TGV Seat Reservation with Eurail Pass

Thanks for the reply. Have you used this site in the past for reservations? Did it all go well?

Ignore that advice and other people adding to your stress. Eurail.com will only make reservations for their own customers. RailEurope.com is actually the most reliable source for pass holder reservations. (You could have made them at the same time that you ordered the pass.) I don't recommend booking by phone.

How long will you be in Paris before you want to travel to Basel? Can you go to the station, show them your pass and reserve a seat then? We have done that in the UK when we have had passes. Actually at no cost.

Thanks for all the great advice! We ended up reserving a seat through Rail Europe. Looks like we’re all set there.

Ed - that’s great info to know for next time. We’re in Paris 5 nights before leaving for Switzerland. I know this train is really popular in the summer, so wanted to ensure our spot. Will definitely remember this, though, for our next time.

Beware, the rules in the UK and France are different.
In the UK, reservations are an optional add-on, are free, and can be made at any (manned) station.

For French TGV trains, if you buy a normal ticket, that ticket is only valid for the one train listed on the ticket and includes a reserved seat. If you have a pass, you must pay extra to get a seat in that train, which is called a reservation. A "Eurail Pass" is not an SNCF ticket. I am unsure whether you can get these reservations (which only people with passes need) at a French station.
The only sure way is to get the reservation from whoever you bought your pass from, and as soon as possible.

Take a look at this link from the travel tips section: https://www.ricksteves.com/travel-tips/transportation/trains/france-rail-passes#reservations.

If you have the rail pass which is valid in France for riding the TGV, get your seat reservation at the French train station. The worse scenario is that the pass quota may be full, which means if you have a 1st class pass ask for a 2nd class seat reservation. Absolute worse possibility is that you might have to change dep time.

I never had to do (this was always in the summer) that when I encountered the Pass quota, only had to change the class reservation from 2nd class to 1st or vice versa. I had a 1st class Pass for that contingency for crossing from Germany to France or vice versa.