It's not the lack of a degree that's the problem, although many employers will insist on you having one, it's the nationality. Unless you (a) hold a passport from an EU member state, (b) are married to an EU citizen, or (c) already hold a valid work/study visa, then it's most unlikely you will be able to find legal work here. EU hiring law states that employers in the EU cannot just hire a non-EU citizen - they first to prove that there were no suitably-qualified EU citizens who could do the job. As you might imagine, this is not a very likely proposition.
I've explained all this and the possible options in my 'teaching in Europe' guide: http://thirtysomethingteachertraveller.blogspot.co.uk/p/teaching-in-europe.html
If you have any other questions, please don't hesitate to ask.