Maybe don’t leave it until the last minute to plan such trips, in Netherlands it is fine to just walk to the nearest station and hop on any train but that is not the way long distance trains in many countries such as France work.

French international high speed services are particularly bad as they have high reservation fees and small quotas for interrail.

For your journey, book a TGV reservation, either at a French station or at b-europe at this link https://travel.b-europe.com/eurail-ge/en/booking-tgv?#TravelWish

to Bellegarde (Ain) it will be €20.

From there take a series of trains that do not require reservations changing at Geneve (Cornavin) and Visp. This connection runs hourly.

There has been a message on the Interail website for months now that it is important to make reservations well in advance for the summer as many people will be travelling by train. 

If there are no seats left on the high speed trains, then you either need to travel with the reservation free slower trains or change your travel plans completely. 

There are reservations available on multiple trains for the connection I suggested as I check these before posting,

I didn’t check the direct Paris-Switzerland TGV as the quotas make there very unlikely to be available at short notice.

@Marjelle Wouters There's no quota on the TGVs. There's a limited number of pass holder seats on the TGV that are sold for 10 EUR. These you can buy on the Interrail/Eurail website. Once those are sold out pass holders can buy seats for 20 EUR until the train is full. The 20 EUR seats can't be bought through Interrai/Eurail.

But that is only for IN FRance-for over the border-the surcharges are far higher and it also seems there are more limited quota (I do not know exact details)-that is why I always suggest to hop over border with FR with local trains.

These young kids nowadays lack any idea of how trains run and how to organise trips-they can only apparently reproduce from these planners and are not even aware that there are ALtrnatives.