The French Revolution had two main outcomes:
1. Spread of Enlightenment ideas around Europe. One of the biggest effects the French Revolution had was spreading the "revolutionary" ideas of the Enlightenment around Europe. During the revolution, monarchies around Europe were disturbed by what was happening in France. For the people to rally together and behead a king meant trouble - what happens if the rest of Europe's lower classes did the same? This ultimately did occur with the Revolutions of 1848 in Russia, Italy, Austria, etc. But the Enlightenment itself didn't just spread on its own like the plague; after the revolution, when Napoleon took power, he attempted to create a French Empire, where he conquered much of Europe for a short time. While his dream of a French Empire failed, his legacy was to spread Enlightened ideas around Europe.
2. Domino Effect of revolutions. During the French Revolution, all French men were freed and considered equal citizens under the law - this included all slaves on the French island of Haiti. Haitians enjoyed their freedom temporarily - when Napoleon seized power, he eventually reinstated slavery in Haiti in order to make more money for his wars across Europe. This resulted in the only successful slave revolt in history. But Haiti wasn't alone in its revolution - much of Latin America learned from Haiti's example, and men like Simon Bolivar and Jose de San Martin led independence movements in South America. Bolivar helped create Gran Colombia (which freed itself from Spanish control but later split into three countries- Venezuela, Colombia, and Ecuador) and Jose de San Martin helped liberate Argentina, Chile, and Peru. So while France gained its freedom from monarchy (until King Louis XVIII took over after Napoleon...whoops!), revolutions sprang up in new world colonies in a domino effect. By 1830, most Latin American countries were independent.