According to the late Sheldon Brown, you can - and he indicated he did without problems on many of his own bikes.

But if I recall correctly, he also indicated he generally avoided doing it on a customer's bike. And it also requires taking the difference into account and adjusting the necessary spindle length to account for the difference in where the crank ends up relative to the bike frame when using the "wrong" taper - which is substantial (about 4.5mm difference, if I'm reading his article on JIS and ISO BB interchangeability correctly).

In short; it adds a major additional complication. I'd avoid that if I could and try it only as a last resort. YMMV.

You could be correct about to OP's BB, if Stronglight, being JIS; dunno when Stronglight changed from ISO to JIS.