Or does each site hold their own specific policy?
On language-related sites the policy is more or less this:
On other sites, I think English is required apart from the cases (not sure if there are any) where someone explicitly makes a proposal in a certain language (assuming it gains participation). But in that case, the Meta would still need to include English (alone or along with the site's language).
Each site has its own policy. But by default, the sites are English-only. If some other language is to be allowed or imposed on a site, I would expect that to be apparent in the original Area 51 proposal.
At the moment, the only sites where languages other than English are allowed are language sites. Those are peculiar in that experts in the site's topic intrinsically know another language. German Language & Usage and French Language & Usage have a sizable number of posts in German and French respectively.
There are now proposal for foreign language sites on Area 51; the most advanced ones are “Stack Overflow in language X”. I would expect these sites to be monolingual (save that meta posts need to be in English or at least have an English summary for Stack Exchange staff for the forseeable future).