Zurich to Freiburg by train - question

Yes, you can just sit anywhere in your class of service (1st or 2nd) on the unreserved train. If they made a reservation on the second leg, then there should be a car (wagon) and seat (platz) number somewhere on the ticket, maybe with the words even more abbreviated than that. If you can't find that, then you do still have the option to sit anywhere that's not reserved (and most seats probably won't be).

The reservation price through DB is 4.5 euros/person, if you check the box to request it while booking. You might have checked that thinking it would cover both legs, but then before the booking is completed, it shows you the same info you quoted above, so you have a chance to change your mind:

Zürich HB
Basel SBB Fr, 17.06.2016 09:00
09:53 IC 764 Reservation not possible

Basel SBB
Freiburg(Breisgau) Hbf Fr, 17.06.2016 10:13
10:55 ICE 370 Compartment type: any;
Location of the seat: any;
Area: any

Swiss and German railways have different policies on reservations. In Switzerland, you don't reserve (except for a few (~4) tourist special trains and for large groups). You c an sit anywhere on the train that is free.
In Germany, for reduced price tickets on long distance trains (ICE, IC) the tickets are for a specific train, and you normally reserve seats. This should be on your ticket. Look for "Wagon" and "Platz" (coach number and seat number, this may also be in English).

BTW there are THREE Freiburg's, one in Switzerland and two in Germany (full names "Freiburg in Breisgau" and "Freiburg an der Elbe"). From your explanation of changing at Basel I assume you mean Freiburg in Breisgau, but if you just ask for Freiburg when you are in Switzerland, you are liable to be directed to a train for the Swiss Freiburg.

Thanks for the great information - explained a lot -