The game is multi-language (french,english,german).

I haven't tried them but I also have the option of Spanish and Italian.
There should be a "Language Settings" program in the start menu to allow you to change it.

There is a small program for changing the language; I still have the problem it doesn't seem to work, though.

While downloading EAW here at GoG, different language versions are offered.

I downloaded and installed the English version.

In order to have the program switch to another language, do I maybe have to download another language from GoG and then install it into the folder of the English install or something?

Forget about the program, will not work with mods.

For FOC (forces of corruption) :

Edit the properties of the shortcut to the following:

"D:\GOGGames\Star Wars - Empire At War Gold\EAWX\swfoc.exe" LANGUAGE=GERMAN

If you want to run a mod (so long German is supported / I used as an example YodenMod which does NOT support German :( ):

"D:\GOGGames\Star Wars - Empire At War Gold\EAWX\YodenMod2015.exe" LANGUAGE=ENGLISH

So with different shortcuts, you can have different languages ;)

For EAW:

"D:\GOGGames\Star Wars - Empire At War Gold\GameData\sweaw.exe" LANGUAGE=GERMAN

Have fun, there are some good mods around ;)

Thanks, I will try the shortcut-solution tonight!

Back when I "only" had the disc version I was really liking the Youtube videos I saw of the English language version but the German version is actually pretty good and being able to change as I like will be great.

Ich mache es kurz habe EAW Gold Pack über Galaxy installiert bin in den Installationsordner gegangen unter Mehr -> Installation verwalten -> Ordner anzeigen und dann die language_setup.exe ausführen Sprache auswählen. Viel Spass