Unless I'm mistaken, it is the same sound as the R in German, Yiddish, Danish,and Swedish.
There is not a single R-sound in French. There are at least two rhotic sounds considered "standard": [ʁ] and [χ] (voiced and voiceless uvular fricatives respectively), and not long ago the Paris dialect had a uvular trill [ʀ] instead (listen to Edith Piaf). But French is not only the educated standard or the Paris dialect; in Southern France older speakers still use an alveolar trill, as in Quebec.
It seems that uvular R is not originally Germanic, and there is no evidence that Germanic languages influenced French in this sense. Some believe that the reverse may have happened (that uvular R in German was borrowed from French) but this has also been contested.
The guttural pronunciations in French are attested only since the end of the 17th century, and only becomes common in the 18th. It's clearly possible that both French and the Germanic languages (as well as many others) evolved their uvular sounds independently.
In the French SE post the question starts by saying that "in every romance language, except French, the phoneme /R/ is an alveolar trill [r]", which is wrong, since Portuguese also has a variety of guttural (uvular and velar) realizations of R.