Why not just a menu of the written-out names of the languages, with each language name in its own language? "English", "Deutsch", "Português", etc. Depending

Why not just a menu of the written-out names of the languages, with each language name in its own language? "English", "Deutsch", "Português", etc. Depending on how many languages you're supporting, you might just make it a short list of links up in the header, at least until one is selected.