Hey Louise,
If you come on a long-stay visa, you can apply for a Patent. It's a number meaning you can work as a freelancer, billing people for your services. That way, you could work in a couple of language schools, or give private lessons without having to go through the process of obtaining a work visa (a long process).
The only thing is, I think with a long-stay visa (without work - meaning you promise not to work for a salary) you need to provide proof of sufficient funds...
You'd better look into it all.
Good luck,
Megan