Hi, in your case I would look where you have to chage from the TGV to IC in Switzerland and only book via Eurail the TGV train. For trains in Switzerland reservations are optional (*except for scenic trains), but mostly only tourist make reservations. Locals not.

Check here where you can buy reservations for TGV Lyria and how you can avoid this trains and save money:

It is straightforward - There are no direct services form Paris to Luzern and you only need to reserve the journey from Paris. If you book from Paris to Strasbourg or Mulhouse and then take regional trains into Switzerland (Basle) this will save you from the more expensive cross border fee for Paris to Basle.

You can easily split multi train journeys and then reserve those trains one at a time.

It also may be that there are no seats available on the Paris trains but that is easily checked on the B-Europe site for domestic TGVs.

https://travel.b-europe.com/Eurail-GE/en/booking-tgv#TravelWish 

It appears all the afternoon trains on 4 June are fully booked but plenty of availability on earlier trains to Mulhouse.

You can also book TGVs on this site but will need a Pass Cover Number 

 

Here is a good route with availability :

- Paris-Est - Strasbourg 13:55 - 15:41 20€

- Strasbourg - Basel SBB 15:51 - 17:09

- Basel SBB - Lucerne 17:16 - 18:30 OR 18:03 - 19:05 if you prefer

The TGV at 12:52 from Paris-Est would cost 10€.

Use Yorkie's link to book.

The TGV to Basel has a very high seat reservation fee of 37€ (2nd) or 70€ (1st class). The 14:20 TGV is full in 2nd class anyway.

Thanks for all your help and response. Due to limited time I book seats on earlier train, but not through Eurail site but by calling an SCNF service team at +33 184 94 36 35, this train was €20 per person reservation ticket. The Eurail site have some issue with booking train with seat reservation. I tried earlier trains and later trains