Probably because it's to determine which tyre fits, not to determine the size of the rim. Slightly wider or narrower tyres will fit the same rim. There was a huge table beneath this picture with all kinds of sizes and more Dutch words, so I didn't copy that. A C/P of a relevant part didn't work either so here is the link. The relevant part starts at ETRO sizes 35-622.

The 'Stadsfiets' is the one from the picture and that has been the most regular upright Dutch bike with those tyres for decades. The regular upright French bikes are usually a bit flimsier with narrower tyres, just as the sportier Dutch bikes above the stadsfiets. So the 700x35 C fits as a replacement for a 35-622 too. The next French size, 38, might not fit if you replace a 1 3/8 because the fender stays are in the way. So I guess the table and the picture are playing it safe, it tells what does fit and not what might fit. I recently put on 47-622 to replace the 1 3/8 but simular bikes might have less clearance and an LBS wouldn't think I left enough clearance anyway. The width in both ETRTO and French is the width between the walls of a tyre full of air, not the width of the bead.

Appearantly the C in French stands for 'jante a croche', which as I understand it is a 'hooked rim', there are also B's but I have no idea what that stands for. Logically the height of all French tyres should be about the same at 700 - 622 = 78mm, or 3 inch. That's not right, so the 700 is probably about the necessary space in the frame, including fenders and some room to tension the chain. Initially I assumed the reason those old sizes use the outer circumference of the wheel including the tyre was to calculate the right gear ratio's for the desired metres of development, but that can't be the case with the French sizes. At least the Dutch (copied from the English) sizes give the heigth of the tyre also. It's probably just typically French: they invented the metric system but lost interest afterwards, didn't bother with it's precision and just used a nice round number.

My conclusion is that ETRTO works very well as long as you or a webshop don't let the other sizes interfere, and it works together with a tape measure contrary to the others.