The problem you have with your freeview box is that it is likely to be DVB-T - i.e. it's a digital receiver, but only for programs through aerials. It might pick up some channels, but you'd have to
retune it. Most people in Baselland and Baselstadt get TV via cable, not by aerial.
If you do have a cable provider already in your apartment - which is quite likely in Basel - then you need to plug your tv into that. You'll probably find you have some analogue programming. To access digital TV, you'll need to buy a digital receiver for cable - DVB-C. Depending where you live, you may have digital TV supplied via cable for free already. I'm in Binningen, and my provider gives me BBC1-4, ITV1-4 and a whole host of other channels, for no additional payment. I know people who live in Baselstadt, who pay a small fee per month to get these channels to their provider - but got a "free" receiver with recording capability built in.