For what it's worth, Wikimedia's Universal Language Selector library has hooks for doing this:
https://www.mediawiki.org/wiki/Extension:UniversalLanguageSelector
See the function getFrequentLanguageList in resources/js/ext.uls.init.js . Direct link:
https://gerrit.wikimedia.org/r/gitweb?p=mediawiki/extensions/UniversalLanguageSelector.git;a=blob;f=resources/js/ext.uls.init.js;hb=HEAD
It still depends on the server, or more specifically, the MediaWiki API. The reason I'm showing it is that it may provide a good example of getting all the useful information about the user's language: browser language, Accept-Language, geolocation (with getting country/language info from the CLDR), and of course, user's own site preferences.
