And Germany would have a second Austria in the German-speaking part of Belgium?
Hmmm...I'm trying this now but it doesn't sound like @Pacifica's yet. Here, I'll post another audio file:Theoretically, it should be a rounded-lip sound as well.
As I have written above, the sound in eux, /ø/ (German ö) should be an é, /e/ (as in passé or like the German e in Leere) with rounded lips.
The sound in orgueil, /œ/, should be an è, /ɛ/ (as in crème or like the German long ä in Ähre) with rounded lips... well, I'm not French (and neither are you ... but you seem to know the language quite well), but maybe you can try it: the difference between è and /œ/ should really just mainly be the position of your lips.