Two points. I'll address the second point first. There absolutely is danger in using the wrong crank puller. And just because it is French doesn't necessarily make it correct, since not all French cranks were the same. There, I tried to make the point as forcefully as possible. To clarify: There are three different crank-removal threads - 1. most English/Campy/Japanese, 2. Stronglight, and 3. TA. (There may be others too but if so they weren't common.)

TA cranks are not like any of the others and their tools will not fit each others' threads. Unfortunately English/Campy/Japanese and Stronglight are almost the same. Stronglight used a thread with just a bit larger diameter than E/C/J, so if you try to use a Campy or Sugino or other "English" thread tool on a Stronglight crank you will strip the threads. DO NOT TRY IT. To make matters even worse, at some point in the early 80's, perhaps '82, Stronglight switched over to the common E/C/J threading. I'm not a Stronglight expert and perhaps someone else can be more specific. Anyway, you can tell which one you have by how the tool fits. If the threads seem loose, then you are trying to put an E/C/J tool into the earlier Stronglight threads.

But this is a moot point because you need a TA tool anyway.

About the gearing, our Peugeot is an '82 and it came as a 15 speed too. In fact, I would have thought that by the late 80's most everything would have gone over to 6-speed rears. Those stem shifters on your are what make me think it is early to mid-70's.

One of the bike magazines back then did a comparison of the Gitane, the Peugeot TH8, and a Motobecane (I think it was). It was available on the Web somewhere but I can't recall exactly where. You may be able to Google it. It may give you a clue about years.

Welcome to BF!