Hi DavidSi
If you have a valid 1st class ticket at the normal fare, which is also valid for travel in Switzerland, and you have not reserved a seat for this part of your journey, then the answer is yes: you can simply take an empty seat on the train. For other details like train number, departure time, platform in Basel etc. you could consult our online timetable: www.sbb.ch.
But I would advise you to definitely still check directly with DB, since you got the tickets from DB.
Thank you for your message and have a nice week. EllenvS.