The Storming of the Bastille is normally considered the opening volley of the French Revolution. France had been in terrible shape because of lavish expenditures by Louis XiV, primarily on foreign wars. Louis presumably said on his death bed, "I have made war too much." French society under the ancien regime consisted of three estates, clergy, nobility and peasantry (translated "everyone else.") Only the third estate paid taxes, the clergy and nobility were exempt. The French Monarchy had raised money by selling titles of nobility (creating so-called "nobility of the robe") whose recipients were themselves free from paying taxes as were their heirs in perpetuity. The end result was an increasingly smaller tax base with increasingly higher taxes.
Louis XVI was forced to call a meeting of the three estates, the Estates General, which had not met in over 100 years to ask for an increase in taxes. The three estates each voted separately, and the first two always easily outvoted the third. When this appeared to happen again, the Third Estate fled from the meeting and formed a new government known as the National Assembly which passed the Declaration of the Rights of Man. It provided for equality before the law and many civil liberties. This was the birth of the French Republic. Louis XVI and his Austrian wife, Marie Antoinette, attempted to flee the country in disguise, but were caught and imprisoned. They were later beheaded for treason.
The revolution itself did not solve all the problems of the people, particularly the working poor known as the sans coulottes. It appeared that another revolution was at hand; but the Jacobins, a radical group in the Assembly, instituted a Directory to maintain order. The head of the Directory, Maximilien Robespierre, was determined that there would not be another revolution. Hundreds were arrested and guillotined; but eventually Robespierre lost the support of the Assembly and was himself guillotined.
Incidentally, the Guillotine was developed by a committee headed by a dentist, Dr. Guillotin. It was thought to be a more humane way of execution, as close to painless as possible. It was so abused, however that Dr. Guillotin's family changed their name.
Subsequently, a large group of nobility marched on the Assembly, apparently ready to overthrow it. They were stopped by a "whiff of grapeshot," that is cannon fire, by a French General known as Napoleon Bonaparte, who soon took over the government and instituted the French Empire.
The French Revolution was the revolt of the Third Estate (the poorest French citizen) against the Monarchy.
The representatives of the Third Estate revolted against Louis XVI, king of France, during the estates general meeting in June 1789.
They declared themselves a National Assembly and wrote France a constitution.
The revolt then spread all over France. The Bastille was stormed in July 14th, 1789.
The Monarchy was overthrown and France became a Republic in September 21st, 1792.
Finally, the revolution ended in a blood bath with the Reign of Terror in 1793-94.
You will find a good summary of the different stages of the French revolution as well as some biographies of the main characters in the website provided.