Today is a national French holiday called Bastellie Day from what I understand it is similar to what we celebrate as the 4th of July. According to About.com Bastellie Day "commemorates the storming of the Bastille, which took place on 14 July 1789 and marked the beginning of the French Revolution. The Bastille was a prison and a symbol of the absolute and arbitrary power of Louis the 16th's Ancient Regime. By capturing this symbol, the people signaled that the king's power was no longer absolute: power should be based on the Nation and be limited by a separation of powers".
It marked the end of absolute monarchy, the birth of the sovereign Nation, and, eventually, the creation of the (First) Republic, in 1792.
Bastille Day was declared the French national holiday on 6 July 1880, on Benjamin Raspail's recommendation, when the new Republic was firmly entrenched. Bastille Day has such a strong signification for the French because the holiday symbolizes the birth of the Republic
Source Credit: About.com