IF you had found the oebb hint on the big list on howtodo RES all by youself+cheaper too-which dear anna fra sverige links all new posters here into-then just read on untill you find this. CanNOT be done direct online-have to call SNCF.

HINT: these trains overborder have about the highest surcharge there is-so save money, not time, and use it only on a domestic FR part and get there on local trains. In the Swiss a RES is unneeded. Even though as far as Bsl should be domestic, the app will always set Bsl in Swiss and hence make it expensive. Use it till last stop in FR-I think Mulhouse-and if sneeky enough just stay in that seat, if not, change there to TER.

Here is some useful information from the experienced travellers in the Community regarding both planning, reservations and activation of pass and travel days. 

 Planning

The rail planner is normally not up to date, as it only is updated once a month, so to be sure of the time table you better check the timetable and availability on the websites of the national railways. The bigger national railways, like DB (Germany) SBB (Switzerland) and ÖBB (Austria) cover several countries. 

 Reservations 

The advice from the experienced travellers in the community is to use other ways to make reservations than the Interrail/Eurail website.  You can look at the guide in the link:

https://community.eurail.com/train-connections-reservations-47/how-to-get-reservations-105

If you, after having looked at the guide, have questions about how to make specific reservation, please give your travel details (departure date, time and route) preferably in a new topic, and you will get advice.

Please note that Interrail/Eurail charges an extra fee of 2 EUR per person and train in addition to the fee for the seat reservation.

 Activation of pass

During the activation process, when you choose the start day of the validity of the pass, the first day of the validity period is automatically made a travel day, even if you don't enter a journey, the advice is therefore not to activate the pass before the first travel day as you only can deactivate the pass before 00.00 on the day the validity starts. If your travel plans change in the last moment you will loose travel days if you have activated the pass in advance.

It can be wise to make a test and activate the pass with a start date well in the future and then deactivate the pass immediately, just to see that everything works.

 Activation of travel day

The advice from the experienced travellers in the community is also never to activate a travel day, that is connect a journey to your pass and create the QR code, until just before boarding the train, otherwise you might loose a travel day if your travel plans change in a late stage  You can't delete a travel day in the past. A travel day can only be deleted until 23.59 CET the day before the travel day.

Please write it down somewhere since it seems I have to repeat myself several times: TGV Lyria reservations can be done online via Eurail/Interrail.

Thank you for your guidance. Do you know how long it takes for Eurail to get back to me regarding the refunds/rebook? Because I want to make sure that I get refunded before I go ahead with another booking.. It is approximately 10 days to my Paris → Basel leg, not sure how long I need to book in advance and I would hate that I do not get a reservation on board the TGV Lyria.

Yes I knew that. I have already done so through Eurail, the payment got through but the confirmation email did not come, the Reservations Overview also did not show anything at all. I have already raised a ticket, that’s why in the mean time I was looking for alternatives in case Eurail support takes forever to process my refund/rebooking. Appreciate your advice anyway, thank you!

My comment was for @mcadv, who has claimed multiple times (including in older topics) that this isn't possible.

Eurail may take some time to process the refund but if you request a refund, it will come.

Unfortunately, this is the only website where TGV Lyria seats reservations can be booked online. Other options are calling SNCF (or NS, NMBS/SNCB, SBB) or booking at a ticket office once you're in Europe.

You should make the new reservation ASAP and then consider the advice from @mcadv to only make the reservation to Mulhouse to avoid the higher cost of a border crossing TGV. 

The refund for the non delivered reservation, which you need to contact Customer Support for, will most likely take several weeks to get.

Use this form to contact Customer Support. 

https://eurail.zendesk.com/hc/en-001/requests/new