It seems that Julius Caesar ( Jules César) followed the advice of the Egyptian astronomer ( l'astronome égyptien), Sosigènes ( Sosigène) who had explained that the year had 365.25 days. Julius Ceasar decided to have 365 days in the year, divided into 12 months, with one extra day every 4 years. This extra day was fixed after the 6th day before the March calends (les calendes de mars).
But where does the word bissextile come from? This extra day in Roman time was called bi-sextilis which means the 2nd 6th day ( le second sixième jour). It is easy to see how bi-sextilis could become bissextile in French.
Cartoonists enjoy playing with this notion of 29 days in February, like Philippe Gelück, the very well-known author of Le chat:
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