I have never, understood the quinze jours description of a fortnight. It is usually said by someone going on vacation/holiday and is vraiment stupide.

Sacre bleu! Ce n'est pas stupide, tout alors.
Consider.
A fortnight is fourteen nights, yes?
A night stretches, more or less, from sunset to dawn (or from when you go to bed 'til the time you get up - a slightly more dodgy proposition for this argument)
Normally speaking, therefore, night starts on one day and ends on the morrow.

Therefore there are fifteen DAYS involved.

Hence quinze JOURS.
Q.E.D.

Whatever else, the French are inexorably logical.