Well I can tell you that "check box" is not North American, neither Canadian nor US, if you are referring to places on forms for making selections. I even thought that the European French might be referring to some sort of safety deposit box since the document was dealing with banking.
We just call the other thing used for filling out forms a "box", no adjective required or desired, as in, "Please check the appropiate box to pay by Visa or MasterCard" with "check" being a verb, not an adjective.
Another friend here thought that "check box" might be a place for storing checks (US) / chequies (Canada).
What do you all think of "mark the appropriate box"? I'm working on an English text for Europeans with English as a second language. In the text "check" is already used as a verb, as in "double check" or "verify." I want to be super-clear.