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.
Wiktionary adds:
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.