Etymonline has this:
Originally pronounced as it still is in only, and in dial. good 'un, young 'un, etc.; the now-standard pronunciation "wun" began c.14c. in southwest and west England (Tyndale, a Gloucester man, spells it won in his Bible translation), and it began to be general 18c.
one and once are pronounced differently from the related words alone, only and atone. Stressed vowels often become diphthongs over time (Latin bona → Italian buona and Spanish buena), and this happened in the late Middle Ages to the words one and once, first recorded ca 1400: the vowel underwent some changes, from ōn → ōōōn → wōn → wōōn → wŏŏn → wŭn.
It is worth noting that one comes from the same source as the indefinite articles an and a (of which an is actually the older form). It is cognate with the Latin unus — whence the French un you mention (and the Spanish un, and the Portuguese um...) — as well as with the German ein, the Russian один, etc.