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Hey I am also a teacher of French language. Currently I am an author of a revision guide book in French
We commonly say English teacher, Arabic teacher, french teacher instead of teacher of english , teacher of arabic and teacher of french as far as I know.
Both are correct. 'English teacher' is more commonly used , usually with the meaning 'teacher of English'. But there is an obvious ambiguity; it can also mean a teacher who is English. On those occasions where context doesn't clear up the ambiguity, 'teacher of English' or 'teacher from England' can be used.