Reinette Franche is a classic old French apple, it is described in Leroy which is the classic French text. To confuse things it was commonly called French Reinette in the US. Reinette Franche is supposed to be a very good apple; I had it growing quite a few years ago but the tree died and I never replaced it. It is a yellowish apple that often has a bit of russet. I had the Geneva (GRIN) version of it and I think its the same as Leroy’s but I never got a positive ID myself.
“Reinette de France” is much less clear what it means as several different apples go by that name. I think by far the most common one circulating under that name is the same as Orleans Reinette: there is a “Reinette de France” quite popular in Belgium which has OR as a listed synonym (and, it looks exactly like it too). There are some other apples with the name Reinette de France that are in France today, an all-russet one and a non-russet one, and I am not sure they ever made it to the US. So my educated guess is a variety of that name in the US will be the same as Orleans Reinette.
I have grown out many of these old French apples and probably 3/4 matched the classic variety I expected, and 1/4 were something else. There are lots of renamings/mislabelings/etc that make it challenging.