the “Alemanni” who lived in modern day Germany and bordered modern day france.

Alemans still live in Baden-Württemberg, parts of Bavaria, Switzerland and I think there's also a splattering in Austria. Basically, High Germans which aren't Austro-Bavarian (same culture, different kingdoms) are Alemans.

“Saksa” is derived from the German region “Saxony”.

That one can be a bit misleading: The modern state of Saxony has nothing to do with the Saxon tribe, the place the title was applied to slowly drifted over the ages. They're much more related to Prussians and Thuringians and even Franks, going all the way over to Flanders and Holland, than Saxons proper. (Holland, not Netherlands).

Here's a rough splotch of where Old Saxon was spoken, which you can consider "core Saxony". At least linguistics-wise it spread quite a bit especially during the days of the Hanse (becoming a minority language as far up as Estonia), but it definitely stops before arriving at a place where "goose meat" means "could you please". Utter gibberish.