French: hein \ɛ̃\
"Euh" is typically the equivalent of "erm"; it signals hesitation [1]. It can also be uttered when a person is surprised.
> Huh is a very specific repair strategy that does not target some part of the statement but rather the statement as a whole.
... and I misread it :). I missed the word repair.
You are absolutely correct with the definition of "euh" - I usually use it when I have doubts or do not agree in a soft way (it then sounds more like heeuuuu...pfff).
As you two suggested, "huh" is tricky to adapt to as a native French speaker learning English, especially American English, because "huh" is not equivalent to any single easily muttered statements in French as far as I know. I would convey the meaning of "huh" in French with: - "ah ouais" (express that I didn't realize something) - "bah dis donc" (express soft surprise or shock) - "mouais" (express soft skepticism or disapproval)
Even those don't quite feel like the encompass the uses cases for "huh".