the library website is pretty bad i think. there is a lot of info missing, i'm not surprised the don't mention the bourse aux livres, i think it's just informally organised by the librarians. it's possible they do the same thing at your library ; if not, you could suggest it.
i admit i have been neglecting my library since i got a liseuse.
i used to go all the time and always have the maximum number of books checked out... but i haven't borrowed anything in months.