[mathieuh]

The French "u" sound is just "i" pronounced with your lips rounded, so the two sounds are very similar.

https://en.wikipedia.org/wiki/Ancient_Greek_phonology#Vowel_...

It seems some varieties of Ancient Greek did have that sound

[stavros]

As far as I know/can see, it was more of an "oo" sound, rather than a ü, but I'm not an expert and you may be entirely correct.