That is likely because the French, just like any other modern nation on the planet, use metric units, rather than the medieval nonsense still common in this country. Heck, even the stodgy British are on metric for decades now...
Anyway, 87-116psi corresponds to 6-8 bar. Otherwise, feel free to use pressure in any of the ranges you quoted above. If you go from 116 to 120psi, that won't blow your tire.