Wait a minute... 
Is it my old and worn ears, or is the woman on the second video totally wrong?
She pronounces the French R sound, the voiced uvular fricative ([ʁ] in IPA), like a Spanish jota, the voiceless velar fricative (IPA: [x].) It's not the same phoneme at all!
It's actually a mistake I've heard more and more French natives commit... at the end of a word! 
That kind of a tendency is called relâchement articulatoire in French :
https://fr.wikipedia.org/wiki/Rel%C3%A2chement_articulatoire
...which does not mean it's considered correct, but barely okay.
Now, that mistake at the beginning of words... I've only heard it from Spanish locutors.
If that woman is a "French and Italian pronunciation expert" as she writes, then I'm an inter-galactic expert in ridiculous women wearing ridiculous hats.