Why does French use the format "4 x 20 + n" (n = 0 to 19) for numbers from eighty to ninety-nine?
The strange construction is a relic from a vigesimal system, i.e. a base 20 number system. This I'm just repeating from the Wikipedia page, but it seems it's thought to be of Basque origin.
The French construction is weird, but the Danish system is up there as well:
50 = halvtredsindstyve ( = half-3rd times 20 = 2½ times 20)
60 = tresindstyve ( = three times twenty)
70 = halvfjerdsindstyve ( = half-4th times 20 = 3½ times 20)
80 = firsindstyve (= four times twenty)
90 = halvfemsindstyve (= half-5th times 20 = 4½ times 20)
Note that these have more common short forms halvtreds, tres, halvfjerds, firs, halvfems. On top of the vigesimal thing, note the strange way to say 2½ (etc), half-3rd. As a bonus, Danish has the ones before the tens, e.g.
93 = treoghalvfemsindstyve (3 and half-5th(4½) times 20).