Ce n’est pas la prise de la Bastille, symbole de la Révolution de 1789, mais la fête de la Nation fédérée du 14 juillet 1790 que la France célèbre chaque année.

The English call it Bastille Day, the French don’t.
Janine from The Good Life France explains better than I  the reason for this in a podcast on everything Bastille Day (you can find it here).

In a nutshell, the Bastille, a prison in Paris, was stormed by the people of Paris on 14 July 1789 which kickstarted the Revolution. A year later on 14 July 1790, the event was commemorated with a one-off national holiday (a big deal in those days). 100 years later, the government decided to have a permanent annual day to honour the French Revolution. It was suggested that the holiday be held on 21 January as that’s the day King Louis XVI was beheaded. Other dates were put forward, but in the end, they went for July 14 – the date of two major events: the storming of the Bastille and the Fete de la Fédération holiday the year after. However, it was never confirmed which was the exact event that was being celebrated! English speakers decided to call it Bastille Day deciding for themselves that of course it made sense to go for the date which had the most drama.