Well, the short of it is that Louis XVI bankrupted his kingdom helping the American Revolutionaries win their independence, and so he called for the first meeting of the French Parliament — les Etats-Generaux — in 150 years. When the parliament met, it soon requested various reforms — elected officials levying taxes, a bill of rights, etc. — which Louis generally accepted. Jefferson was on the ground, even assisting, in the earliest stages, and he hoped that his friends such as Lafayette would succeed in their reform efforts.
After a few years, however, radicals took over, deposed the king, killed the king and his wife (perhaps his heir apparent too), and responded to other countries’ hostility to the establishment of the First Republic and attacks on it by conquering their immediate neighbors. Domestically, the Revolution embarked upon a course of changes in government, each ruling party more radical than the one before, culminating in the infamous Jacobin dictatorship and Napoleon’s overthrow of the civilian government. You can of course find a detailed account of these matters in the Liberty Classroom Course “Western Civilization Since 1500.”
Jefferson seems to have remained confident that all would work out for the best even into the Napoleonic period, which was long after essentially all other prominent Americans had been disabused of that view by events.