Yes, generally need to book notably in advance in order to get a reservation at Les Faux. Alternatively, to give away a bit of a trick, you can go early and eat at the bar (which is common and service is fine).

The current menu (when we went a few weeks ago) is slightly different from what you see online. The prices are generally the same but it appears they dropped some items and added a few new ones to the mains. They also have daily specials and I'm guessing some of the old regular items make a guest appearance on the specials list (eg. The salade frisee aux lardon was no longer on the menu but was on the specials the night we last went).