The typical American would definitely have known about the French Revolution. There were many interactions between the two countries, with the American Founding Fathers supporting and hoping for a French victory in Europe to allow them to push away from British impressment of sailors in the Atlantic, amongst other things. Interestingly they hated Britain, a democracy, so much that they sided with the military despot and tyrant Napoleon, even when founding their new country on the principles of democracy and freedom!

Particularly in those days, the 18th/19th century, many countries depended enormously on overseas trade, and as such the fluctuating state of war, peace and trade between maritime countries made everything everyone's business. It's worth bearing in mind that before the war of 1812 America was largely dependent on the east coast maritime ports for revenue (around 70% of federal income from taxes), whilst having no notable naval force, and so the state of the rest of the world was very important. James Madison/Thomas Jefferson didn't like this and tried hard to isolate America and force trade inwards. They wanted the coast to be the final frontier, no one coming in, no one going out.

The press of the time was just as fickle as it is now and reported on the success and failures of national interests abroad, and the governments had to extend their reach and influence around the globe in order to keep the support of the voting public back home.

On top of this, a lot of the developed western world was, if not a significant global power of their own, a vassal state or colony of a nation that was, and so obviously had a lot of contact and interest in overseas situations.

Obviously the average member of the public wouldn't know the minutiae of the lives of foreigners, but at that time a lot of news and gossip would have focused on the state of the world at large - through war and trade.