Only one train showing, SNCF has many - where are they on Eurail. or Rail Europe?

Also, I reserved seats on Rail Europe web site, for the Train - Paris Gare De Lyon to Basle 19/04 at 14:22 with 1st Class Eurail Global Pass, but received 2nd class reservation.  No 1st Class option was available, but SNCF shows 1st class is still available. 

Are there only a small number of seats available for Eurail Pass holders?

There's no quota.

However it can be a bit tricky to select 1st class on the Rail Europe website. Here's a screenshot from my phone -> you need to click on the price and then select the fare. 2nd class will be offered first as it's cheaper.

Btw there are way more trains actually running between Paris and Basel/Switzerland than those you see right now. They'll be published on 22nd January as well, don't be too impatient haha

Direct departures from Paris at 07:22, 10:22, 12:22, 14:22, 16:22 and 18:22.

I'd suggest you refund the reservations you have right now, it's possible for free. Then wait for Wednesday French time (likely early Thursday in Australia).

I'll also mention that it's a lot cheaper to get off the TGV within France (here, Mulhouse) and continue by TER regional train to Basel. The first fare is 10€ (regardless of the class) and increases to 20€ closer to travel. For 2 ppl you'd already save 58€! ;)

Plenty of departures from Paris to Mulhouse: 07:22, 09:21, 10:22, 11:15, 12:22, 14:22, 16:22, 17:17, 18:22 and 18:50. Looking at a random Saturday in March.

Thanks for that Info.  I have cancelled the Paris - Basle 2nd class booking and I’ll wait till after 22nd Jan to rebook.  Good to know, as I was beginning to panic that all my planning was “going out the window” because somehow the trains were not bookable.

Thanks for your help.