I always keep an eye on http://ja.kampagnenforum.ch/jobs/stelleninserate
but most of the adds ask for excellent German and French language skills.
I do speak German but far from perfect, and just a bit of French.
I had hoped that many non-profit organizations had English as main language as they often deal with international issues.. but that seems not to be the case.

Am I looking in the wrong direction?
I have a PhD in Politics and would love to work for non-profit organizations, but I don't seem to find anything here in Switzerland.
Any advice would be much appreciated.

I'd rather look at the cinfo website: http://www.cinfo.ch/org/index.php

There you can find the jobs from the international NGOS (where english is a/the working language).

Kampagnenfroum is good for finding jobs in smaller/national NGOS where the working language is (quite logically) one of the national languages.

try also

http://www.reliefweb.int/jobs?search...d_job_type-263

and

http://www.unsystem.org/