No reservations at all needed indeed. It would be a waste of money and nobody makes them. Simply hop on and find a free seat.
The only advice I could give you is to go to either end of the platform as they are always more available seats than in the middle. Unless it’s a holiday weekend (17-18.05 or 29.05), trains won’t be especially busy anyway.
Just a suggestion if you’ve got time (adds an hour) : the route via the Old Gotthard Line is simply impressive (instead of the 57-km long Gotthard Tunnel).
- Lugano - Bellinzona 09:25 - 09:43 (already the 15-km long Ceneri Tunnel)
- Bellinzona - Basel SBB 09:59 - 13:56
- Basel SBB - Strasbourg 14:21 - 15:39 (or a later train)
The connection via the Old Gotthard Line is possible every hour, with an easy change in Arth-Gold every other hour.
Edit : even more as you've got first class passes, you don't need reservations (overlooked that)
Btw the SBB app (or website) can tell you the train's composition on the day (and also how busy it should be). You can always check that in advance by searching today's train, shouldn't be much different.
I wouldn’t bother personally but it is up to you.
Only the first leg will be reservable. Basel - Strasbourg will be on unreservable French TER, these run half-hourly and unlike many French TER still have 1st class, if you want to take a break in Basel just hop on whichever you please.
Thanks to all of you. Thibcabe, I’ll look into the possibility of going via the Gotthard line. I don’t mind sacrificing an hour.
Cheers!!!