I speak the language of the speechless (dumb) people.
Just to make sure you've got it, Dan. Andrei meant 'dumb' as in 'deaf and dumb' (taub-stumm) or a "dumb waiter" (stummer Diener), not in the sense of 'stupid' (dumm). So, you'd be more be saying "Ich spreche die Sprache der Menschen, mit dem man mit Händen und Füßen reden muss (weil sie sonst rein gar nix verstehen, da sie unsere Sprache nicht sprechen)"
I understand the name Germany comes from Latin, meaning a brotherly people, an offshoot (to germinate). French call them Allemagne, meaning 'all people' (Alle- all, manner with an umlaut, men. ). There was a tribe called the Allemanni, perhaps a bit like Americans, being composed of 'all men', all ethnicities of men.
My teachers told me the Russian word, meaning dumb, and the Slavs are the people who speak the same word, слово.
The English and all the Germanic people called foreigners, Welsh/walsh, etc. The same as Galatians/Celt/Gual. It is the French spelling, as in Warrany/Guarantee, war and guerre.
The ancient Greeks called us and everyone else 'Barbarians', so we continue the tradition of 'us' and 'them' names.
The language Deutsch is akin to the ancient tribe the Tueti/Tutons who invaded Roman territory. It means 'people' in the old Germanic and IndoEuropean language.