In French, the most common realizations of the phoneme /r/ are [ʀ] (uvular trill) and [ʁ] (voiced uvular fricative). I am able to consistently distinguish them and produce either, and I'm interested in the allophonic distribution of the two variants.
I listened to samples of French words on wiktionary in order to determine which one is used in what position, but I have been unable to come to a definitive conclusion. I am looking for scholarly sources that delve into this topic, or for native French speakers who can distinguish the two allophones to inform me about how they use each.
I think a general trend is that word-initially, we have [ʀ], and also if the /r/ phoneme is next to a plosive, it also seems to be trilled, although not always. In all other positions, I hear the uvular fricative [ʁ] most of the time, most notably intervocally I haven't heard any trilled pronunciations. I unfortunately don't have a diverse enough range of samples to determine the exact details of the distribution. I also expect that it would vary from speaker to speaker and dialect to dialect, which I don't have data on (but a well-informed native French speaker might).
On a side note, I would also be interested in the same question of `uvular trill vs uvular fricative' for other European languages which use uvular rhotics, although I expect that the distributions will be different depending on the language.