First post, and I'm desperate for help on this issue.

I'm restoring a 1770-71'ish Peugeot Mixte with my GF and we ended up getting these Peugeot branded cranks to upgrade from the crappy cottered cranks that it came with. They are Japan stamped on the back of the crank arm.

It's a French threaded BB, and I'm probably going to purchase one from VeloOrange, but I'm unsure of what spindle length to get. Should I just measure the one that came with the cottered cranks and go off of that? Also, does any one know if these cranks are an ISO or JIS taper?

I really want to nail the spindle length on the first try. Any and all help is greatly appreciated. I can't find info on these cranks anywhere online!

That's a Peugeot-branded Stronglight crank, so closer to JIS than ISO. Post-1982 production, so it will use a standard 22mm extractor. You're unlikely to get any useful information from measuring your cottered axle. Perhaps Velo-Orange knows what will work?

Stronglight cranks even though they are stamped japan? I thought stronglight is a French manufacturer?

VeloOrange wasn't much help either, unfortunately.

If they're stamped Japan, they're probably Sakae Ringyo. Also JIS. If really "want to nail the spindle length on the first try," err on the side of too long. That way you should avoid clearance issues, anyway. My experience with converting cottered to cotterless involves sitting down with a big bucket of spindles and trying each one until I find the best fit.

Some (maybe most) spindles are unequal length on either side of the bearing races, so that would give you a 2fer using the trial and error method in those cases.
I have one triple crankset that actually lines up better using the shorter end of the original spindle, on the two bikes I've tried it on so far. The slight extra length on the non-drive-side was not an issue, in either case.

Most Stronglight cotterless, double cranksets from the late 70's and through the 80's worked well with 118mm legnth non-symmetrical spindles.
I believe Sheldon Brown agrees on his crankset/spindle tables on his site..