The initial root cause of the storming of the Bastille, and the subsequent French Revolution, was France's economy. In the late 1700s, the country was in a financial crisis, which set in motion the sequence of events that led to the storming of the Bastille.
King Louis XVI convened a meeting of the Estates General in 1789 in an attempt to implement a new land tax. The tax was opposed by the Second Estate, which represented France's nobility. The Third Estate, which represented the middle and lower classes and thus most of the population of France, was dissatisfied with their relatively low level of influence. They independently formed a National Assembly to create a constitution for the country.
The economic situation combined with a massive crop failure that led to widespread hunger prompted mobs to begin forming in the streets of Paris. Plundering then began, and several grenadiers who had been jailed for refusing to fire on the people were freed by force. The Third Estate formed a militia and raided the Hotel des Invalides for arms. They found guns there but no powder or shot. The Bastille was chosen as the next target both for its stock of gunpowder and as a symbol of the royalty.