English will work fine, but then any language will work fine, as other answers have explained. The fact that English is closer than anything else, with Mandarin as the only real competition, means you might as well start there.
But I think your real problem is that you're thinking too much of en...
personally when it comes to a global government I don't think requiring one national language to be too repressive. In my mind it would be kinda like the examples you gave so instead of hiring translators and what not to attend school away from their local state they just learn Common.
@CelestialDragonEmperor If "requiring one national language" just means teaching everyone English and requiring all government agencies to be bilingual in English, then it's not repressive. But English-only education, requiring people to use English to request a local pothole to be filled, etc., that's a different story. We're only talking "repressive" in the sense of 19th century Italy, not Nazi Germany or something, but it's still more than necessary.
@CelestialDragonEmperor Your point about attending school away from home is a great one, though. If you make it cheap and easy for anyone with the talent to go to university anywhere in the world, universities will gravitate toward using more and more English, which will be another factor in spreading English as a global language. I believe (but I may be wrong on this) that already happened with universities in India—despite the law allowing English, Hindi, or local, first the best universities, and soon nearly all universities, ended up primarily English.
in most cases the Hegemony is laid back and rather supporting of local cultures and customs, but a few things like national language they step a little bit into authoritative. In their mind it's due to a clear single language being beneficial across the board. However on the streets of the Hegemony you would have signs in mandarin, people speaking korean, hear Spanish music, etc. Think of it like how mandarin was used in Imperial china: the language of the bureaucracy, but in this case also the language of the education system. Although I'd assume exceptions would be made here and there.
@CelestialDragonEmperor Canada has two official languages (English and French), people have a right to use either -- certainly whenever they interact with national government (e.g. taxes, passports, law courts), and partially with provincial government (e.g. to attend school in either English or French). Similarly in Wales you have a right to use Welsh. Maybe that's not too onerous, if you want to support multiple national languages as well as a global language.
@CelestialDragonEmperor But is the government stepping a little bit into authoritative because that's what you want for your story/game background/whatever, or because you think it's necessary to make a global language take off? If the former, then sure, make it like 1960s France or 2010s China as far as language is concerned and it'll work at last as well as they did. But if not, I don't think it is necessary.
@CelestialDragonEmperor I may be wrong but I think Chinese was unusual -- that regions had their own spoken languages but they all use standardised Chinese ideograms for writing.
@ChrisW that is true. But Mandarin was the language of well the Mandarins imperial officials across China. I think it's that way today with Mandarin being the language of the government, but not the majority of people in China.
@ChrisW Great point. If the Hegemony treats Wales the exact same way that the UK treats Wales today, they should have the exact same near-universal English proficiency as today. The only potential problem is in areas with too many local (or immigrant) languages, but in practice that isn't a serious problem for most parts of the world today, so it probably wouldn't be for the Hegemony.
@abarnert is it weird to say both? Like the Hegemony all and all is the good guy in my sci-fi, but since I'm doing post cyber punk I feel that making it slightly authoritarian is the way to go nothing Orwellian or fascist, but enough to ruffle some feathers to have debates in universe, however I've made most of the authoritarian bits either out of necessity or with good intentions. But also I thinking having a clear global language might require someone to stamp their foot down.
@CelestialDragonEmperor According to official government statistics, Mandarin is the L1 language for nearly 75% of the PRC (not including Hong Kong). I don't know how far you want to trust those statistics, but the Ethnologue says 70%, and the CIA World Book says it's a clear majority. (However, even "Mandarin" includes regiolects like Jin that aren't mutually intelligible with Modern Standard Mandarin.)
@CelestialDragonEmperor No, it's not weird to say both. Plenty of "good guy" liberal governments have at various times pushed various kinds of single-language enforcement in aid of helping the hicks or the immigrants "get a leg up". I don't think you do require someone to stamp their foot down, but a government that did think so, and did it as nicely as possible but still as firmly as necessary, that would certainly be plausible, and understandable, and wouldn't make your Hegemony smell evil.
@CelestialDragonEmperor If you "stamp your foot down" the way the Académie française does, maybe that's tolerable. They affect (define) what precisely will be taught in schools, which is not a very big deal IMO as long as people tolerate that subject's being taught at all. I suppose countries like France (and the UK) used to have different regional languages, and eventually standardised on their "national" language via education.
@CelestialDragonEmperor In fact, if you want to hint at some of those debates in the background of your story, look up some of the 20th century Dutch arguments about immigrant assimilation. Usually the right talked about "requiring" them to assimilate and the left about "aiding" them, but as far as the actual programs they pushed, it's hard to tell which ones came from which side.
"Obviously you need EU-style freedom-of-movement laws" - no you don't. People don't require free movement simply in order to go on holiday/business between each other's countries.
@ChrisMelville It’s much easier to set up a business deal (especially one that will require people to regularly go back and forth between the two countries) between two Europeans than between a European and an American, or a Mexican and a Honduran. It’s much easier to vacation in six countries in a month when you don’t need to go through customs and immigration every time you cross a border. Making these things easier makes them more common, and the goal is to make them ubiquitous.
I seriously doubt whether Mandarin could be considered as competition to English as a GLOBAL language. While it has many speakers, they're almost all geographically restricted to part of China. English, along with Spanish & French, is widely distributed. The tonality of Chinese languages also makes them difficult to learn as a second language. And then there's the writing system...
@jamesqf I don't think the issue is how many people speak it natively, but how many people use it as a shared L2 language when talking to people with different native languages. And that is pretty much restricted to southeastern coastal China and a few other places in southeast Asia. Even in nearby countries like South Korea, Vietnam, or Mongolia, if you don't speak the local language, you're better off with English or Russian than with Mandarin.
@jamesqf Spanish really has the same problem. It used to be a common shared L2 language between people with different L1 languages in many parts of the world, but it's mostly been supplanted by other languages like French, Arabic, and English. (I have heard a Portuguese and a Brazilian talking in Spanish because they couldn't understand each others' Portuguese, which was pretty funny, but I doubt it signals a general rebirth of Spanish as a lingua franca…)
Discussion on answer by abarnert: Is …
Discussion on answer by abarnert: Is …