I'm a Hebrew speaker, and in Modern Hebrew, there is a distinction between /ʁ ~ ɣ/ and /x/. When I hear French, I recognize that 'r' isn't always pronounced as /ʁ/ but in many times, as /x/.
I tried to think of a mechanism to this and I noticed that in many times the 'r' is pronounced as /x/, it's after a consonant, while most of the times 'r' is pronounced as /ʁ/ it's after a vowel.
For example, I've always heard "tres" (very) as /txe/ and never as /tʁe/, while "amour" is always pronounced as /amuʁ/ and never as /amux/.
Quite strangely, French accent in Hebrew is usually identified immediately since French speakers tend to merge /ʁ/ to just /x/ (meaning that /xatsotsʁa/ - a trumpet, is pronounced by French speakers as /xatsotsxa/)
So, when is 'r' pronounced as /x/ and when is it pronounced /ʁ/?