In France I believe they're government employees. They're paid via taxes in big and medium cities, so free to sign up there. I find them huge, for instance my 300k person city has 8 or 9 libraries on the same municipal network so that everyone is less than 10min away from one by bus or bike. Some are general, other are themed, for instance the music and dance school library is arts themed, there's a children's literature library, and a local history one - but you'll find children's books, arts and local history in all of them.

As a kid in the early 2000s in my village we had to pay 5€/year for books and 10€ if we wanted books, music, movies and video games. In all the cities I've lived in outside of this smallish one (8k inhabitants) it was free. They never really expect you to pay late fees either, you just can't get new books until you've given back the previous ones.