I'm a native Finnish speaker, and as mentioned in the video, we also have u-psilon ('y' in Finnish, not u or u-umlaut). However, the sound may be a bit different from the French one, although it's surely quite close to the German one as far as I can hear. This variability may make it easier to pronounce for different people, because we don't need to have one correct nuance in restored Koine.
I found this possible variation: instead of starting with English 'ee' (like in 'see'), try starting with 'e' (like in 'set', 'dead' etc. but long) or even with 'a' as in the article 'a' or 'an'. Instead of rising the front/middle part of tongue up, as it happens in 'ee', try letting the tongue be relaxed, resting it in the bottom of the mouth. Then round your lips as instructed in the video. These all result in a recognizable 'y' sound in Finnish, although not all of them may sound equally natural if used in speech.
The point is to round your lips and not
raise the back part of tongue. In 'for' or 'far' you raise the back of the tongue; in 'see', 'set' and 'an' you don't.