'The TEFL' doesn't mean very much as there are many places offering courses with this name, and the CELTA does carry some weight despite the many criticisms of the course content. I'd go for that as a starter as itr is recognised the world over. There are Americans working in the EU, so it's possible, but it is easier to employ EU citizens so you may have to look around a bit more. There's often an element of luck and of being in the right time and place- positions often come up at short notice and then nationality doesn't matter. Where positions are azdvertised in a more leisurely manner, you may find that preference goes to EU teachers.
- For Teachers