The term you are looking for is "Latinized" or "Romanization" which means translating a name or piece of text from a native script in to the latin script.
And I believe that Hungarian should fall in the same group as English and French since it's compatible with the Latin alphabet. If you're using their Latin-based script instead of the Cyrillic one, that is.
Unfortunately most people won't understand that Latin alphabet means the English AaBb etc. So you can't use that as the label.
Instead, I think the best choice would be "International" and "Local".
Global is not terrible, but not actually -everyone- speaks English so using that term makes the label feel bigger than it is or should be. And for many workers that live in the country, their native language is the primary and English the alternative. Which means that the term "alternative" can also be quite confusing. "Local" on the other hand works for language, and the type of businesses and employees you're dealing with.
So calling it "International" and Local" makes more sense from a business and demographics perspective. It makes the perceived importance gap between the required and optional form languages feel smaller, which is closer to the day-to-day reality. A a bonus it is not quite as insulting to local workers - in fact it might even feel like a feature implemented for them as a customization.
And the term "alphabet" isn't quite correct as Chinese is logographic. ( https://en.m.wikipedia.org/wiki/Logogram )
So I would look for alternatives. If it's a single button you could use "International script" and "local script" but if you have both languages visible in the same screen I would name the headers similar to:
Which again has the benefit of feeling like an addition because you can now add in a local company address as well as an international head office.
Lastly some notes;
-this question might've been better for a language focused community such as english.stackexchange.com
-you asked the question yesterday and apparently decides on terms that same day. This site isn't an instant helpdesk so next time try to plan ahead a bit ;) I've decided to answer anyway since there might be others with the same question.