Other Languages?
You do not have to be a native speaker of English for the JET program because they do seek other languages. Look specifically at the list of participating countries here
The JET Programme - Aspiring JETs - Participating Countries to see if your country is on the list and what the embassy says about visas and blah, blah, blah
NOVA will hire native speakers of almost any foreign language. There are a few private French eikaiwas, and I believe Aeon Language services may hire a few of the others as well. But there are more jobs for English teachers which is why it is almost all you ever hear about.