All I can think of is …
If the menu doesn’t save different settings on the 2 different multi-lingual pages …
Then a possible hack / work-around would be add 2 menus to the page. Setup each with appropriate settings, then try adding code to the page so that if either: word in header = ‘some word in english’ then show ‘this menu’, or else show ‘that menu’.
Do you know what I mean? (Just a theory, have not tested it nor created anything like it for the multilingual pages/settings)