Strictly speaking you are right Vero, but in certain parts of England ‘thou’ is still used routinely (Derbyshire, the border of which I come from, and South Yorkshire) though often reduced to ‘tha’. But not in its French context, nothing to do with familiarity, those who use it address everyone that way.
A funny offshoot of the British not having separate plural and singular words for you is in Glasgow and Liverpool (perhaps because of heavy historical Irish immigration in both cities) many people use ‘youse’ when speaking to more than one person.
I unloaded in Barnsley once, and was asked to reverse to a dock between 2 other trailers. The man stopped me and shouted ‘owd l’ha oppen tha dooers?’ (how will you open your doors?) not realising that mine were bi-fold and had plenty of room. But I had to ask him at least 3 times to repeat himself as I couldn’t understand a word. I felt quite embarrassed because I knew he was speaking English, but it sounded even more unintelligible than my poor effort in print to represent it. In the end he spoke very slowly as if I was a foreigner. Set me in good stead for coming to live in France, where I am.