There is no direct train from Paris to Bern. Book Paris to Basel and take the first Intercity to Bern (optional reservation - in Switzerland only tourists reserve seats)

It looks like the reservations module is struggling again. Either book late at night or during the day. Or call SNCF (press #85 for English). And indeed: in Switzerland, almost nobody books reservations… just book the TGV from Paris, that's enough.

Thank you for your responses. 
forgive me I am new to inter rail . Am I right in saying I’ll pay for my reservation , then when I get the other trains the cost is covered by my inter rail pass?? If so how does it work if I call ? Or do you mean to call for the trains where I have to reserve? 
I have a 7 day inter rail mobile pass 
 

Yes-well over 90% of all trains running are completely RES free-just board and find seat/or stand if you are too shy to ask someone to move luggages away from empty seat. AND wear MASK still in many countries. The pass is your ticket. Yesterday I used 8 trains like that-and nr 9 was an overnight with access control.

BUT about any newbee here wants exactly to ride the few trains that are hopeless to REServe as they have tiny quota for passholders.

From P to BERN: BEST way is to take the Geneve bound TGV as far as FRASNE and change to local siwss train onward-via Neuchatel, from there. Not all TGV have this direct connection. Use planner of bahn.com and split up in these segments for complete overview.

All in all in fact about very much the same as you would go by train in GB-except that some countries (notably the superfast in FR-ES-IT) have mandatory REServ for there trains.

Thank you .