Welcome to the forum.
Well, that's going to be the problem I expect. Still it never hurts to try, but be aware that the emphasis here is for employers to try and hire people who already have a permit to live/work here so not having one will put you down the list.
As an EU national (for now) you can come here for up to 3 months as a tourist and look for work. If you don't find a job in that timeframe you can then apply for an L job seeker permit for another 3 month period, providing you have sufficient funds to support yourself.
Here are some websites to try:
www.jobs.ch www.jobup.ch www.monster.ch www.monster.co.uk (yes they have Swiss jobs advertised, you just need to change the location to access them)
You/he might also look at the possibility of a concubine permit for you. It's for unmarried hetreosexual couples, but he would have to agree to be financially responsible for you for 5 years, not all cantons offer this permit and it may be that your relationship hasn't been going long enough for this to be possible.