What were the lasting effects of the French Revolution on global history?
The French Revolution, unlike the American Revolution before it, was the first example of a powerful monarchy being overthrown on its home turf, not by another monarchy, but by its own subjects. This event sent shockwaves of fear and panic across Europe and put every monarch on notice that his or her power was not absolute, as has been assumed for centuries, and that when a downtrodden, desperate people demanded reforms, even a king with an enormous army and vast wealth could not ignore those calls for change.
The French Revolution not only put monarchs on notice that they had better listen to their subjects, which was an absurd notion at the time, but it also sent a clarion call to the burgeoning working classes, merchants and peasants of the world that they did not have to resign themselves and their children to a life of oppression and political impotence. If those people organized and were willing to risk their lives for change, then they could perhaps prevail on even the most arrogant of monarchs to address their grievances.
As a result of the French Revolution, the British Monarchy and aristocracy accelerated a push to reform how peasants could use common land, and gave ordinary citizens more power to elect members of parliament's lower house (The House of Commons), so that ordinary English citizens could seek redress for their grievances without overthrowing and killing the royal family. These kinds of reforms began to take root in other countries worried about revolution: the Netherlands, as well as various German and Italian principalities.
Yet the French Revolution also had a chilling effect. As members of the National Assembly and Triumvirate, as well as ordinary Parisians, were picked off and publicly executed by Robespierre's ironically-named "Public Safety Committee," which became the instrument of power under his Reign of Terror, advocates for revolution in other countries looked on in horror as the reformers became worse than those they had deposed.
This legacy of revolutionaries becoming more despotic than the monarchs they replaced also had a thunderous impact on global history. Counter-revolutions like the ones that shook France over the next century gave many reformers pause, and also shored up support for certain tyrannical monarchs like the Russian Tzars. Additionally, many intellectuals and merchants in various countries across Europe saw how revolution could lead to even worse outcomes, and began to seek change through more democratic means such as constitutional monarchies.
In other cases, despotic monarchs used the example of France to convince enough of their dissatisfied subjects that a heavy-handed king was better than the murderous chaos of mob rule. So while the French Revolution made the idea of overthrowing unjust monarchs seem possible for first time, it also gave serious pause to those who would do so, and in the long run, forced would-be-revolutionaries to refine their theories of democratic government, and to look towards the American system for guidance rather than to that of the French.