Why was the French Revolution important to world history?

Three reasons:

1. Louis XVI, the French monarch bankrupted the french treasury by engaging in American War of Independence. He then levied high taxes on the general public to cover the war cost. This was classic failure of public relations on the part of the monarch, where the common people believed that the king levied exorbitant taxes to fund his own and queens out of the bound lavish lifestyle at the expense of the citizens. This is the most common example cited in modern times showing that improving public relation is so much important for politicians.

2. French Revolution was the first incident in Europe where a reigning monarch was forced out of the throne by common public and executed for treason against the country. This was historic because at that time monarch and the country were synonymous and treason was basically defined as betraying the monarch.

The other monarchy of the Europe were completely shocked by the event and fearing similar revolution in their countries they granted more power to the people's democracy. Thus, french revolution was the catalyst towards democratic reform in other European countries, and the other parts of the world especially, South America, people rose against their European monarchs and gained independence.

3. Again, when Napoleon took over France few years later and proclaimed himself the Emperor, that was the first modern instance of fragile democracy being overtaken by a dictator. This sets an example on how a democracy can be hijacked by a dictator.