As a French person who studied the American revolution, it seams that the Marquis de la Fayette is more of a hero of the American revolution than the French one.
In the musical Hamilton by Lin Manuel Miranda, La Fayette seams to wish to be anti-monarchist and free his people. From what I understand he seemed more on the side of the king. Did he wish for a more British like constitutional monarchy, did he support the rioting in Paris or is it more subtle than that?
Oh LaFayette. I feel for the guy. I think the most apt, one-word description I've heard of him was that he was an "idealist"; I agree whole-heartedly.
LaFayette is sometimes called "The Hero of Two Worlds", but as the French Revolution became more radical he was seen as far more of a traitor than a hero, and in 1793 could plausibly have been called the most hated man among the Revolutionaries. His reputation certainly was more pristine in America than in France.
LaFayette was emphatically NOT anti-monarchist, in fact very few people in France during the Revolution were anti-monarchist. LaFayette was, like most of his fellow liberal nobles, in favor of a constitutional monarchy that would guarentee rights for the people, and enable capable men to assist in running the country. It's a common fallacy that the Revolution was from the start about instituting a Republic. It wasn't until the Flight to Varennes that a Republic was championed for by even the most radical of revolutionaries, and even then many played around with the idea of a regency government around Louis XVI's son Louis XVII rather than a Republic. Republics were seen as messy, chaotic, and unwieldy. Constitutional monarchy, on the other hand, was seen as strong enough to maintain order, while guarenteeing rights that could be deprived in an aboslute monarchy.
LaFayette was fully supportive of a constitutional monarchy. He wanted the order and stability that it would bring, along with the rights it would guarentee to the people in its constitution. LaFayette was also a prime mover behind the Declaration of the Rights of Man and of the Citizen, which guarenteed certain civil liberties to the people. It is worth noting however that under the system LaFayette champtioned, (the so-called Constitution of 1791 that was undermined when Louis attempted to flee Paris in the Flight to Varennes) there was not universal manhood suffrage. Instead, this Constitution made the distinction between "active" and "passive" citizens. "Active" citizens were classified as men who paid a certain amount yearly in taxes-- this therefore excluded any sort of day-laborers or poor farmers. These groups were instead termed "passive" citizens, and they were not allowed to vote or join the National Guard. The idea behind this dichotomy wasn't anything new: it was merely the idea that those without a real 'stake' in the country couldn't possibly have a say it how it was run. The fact that LaFayette supported this system shows that he was not a screaming liberal, but rather a moderate, reform-minded man who wished to see things progress in a way that would effect real political change, without hardcore social change.
As the Revolution became more radical, Lafayette became more despised for his moderation, until he finally deserted his post and slipped across the border to Austria. Fast-forwarding, LaFayette will again rise to prominence after the so-called July Revolution which toppled the reinstated Bourbons. In this 1830 revolution there were called to reinstate the Republic, however many men feared the return of the Republic, associated as it was in many minds with the Terror, and therefore these more cautious men put forth the idea of instead elevating to the kingship Louis-Philippe, son of "Philippe Egalite", the duc d'Orleans who was executed during the Terror, but had been a staunch supporter of the Revolution and even a regicide, voting for the death of Louis XVI. The Orleans were a cadet branch of the Bourbons, and next in line for the throne should the Bourbon line die out (or prove insufferable to the people, as it was).
In making this decision between another shot at a Republic or Constitutional Monarchy, LaFayette is typically seen as the crucial deciding factor, though how big a role he played is sometimes debated. LaFayette was seen as the voice of liberalism, and venerated at this point in his life by many of his countrymen, who idolized the revolution of 1789-1792 and despised the revolution (and the Terror) of 1793-1794. Into this mix, LaFayette would be a large weight that would easily swing public opinion towards either form of government. Therefore it's said that, when LaFayette threw his support behind Louis-Philippe and embraced him publically on a balcony in front of crowds at the Palais Royale, he had given the future king his "Republican Kiss", signalling to the people that he fully supported the Constitutional Monarchy over a renewed attempt at a Republic.
In all of his actions, LaFayette may seem like he was facilating between liberalism and conservatism, but that's only because we tend to present things in extremes. LaFayette was what could be termed a "Liberal Moderate". He occupied a middle ground that supported the Enlightenment idealism of liberty, fraternity, and equality. He supported a constitutional monarchy that would provide justice and order to the people. He abhored mob violence, but seems not to have wished to address the social aspect of the unrest. He believed in a hierarchy based upon merit, rather than birth. His idealism meant that he wished to address the political questions without really addressing the social questions, and he would always be dogged by the lower classes of Paris getting out of hand. He was part of the group of liberal nobles who believed that in answer the political question and pursing Enlightenment ideals that the social problems would gradually be worked out. This ran counter to the ideas of 1793-1794 that sought to address the social questions first and in often radical ways that LaFayette did not agree with. We see in 1830 that LaFayette did not blindly believe in Republicanism, and that by the end of his life perhaps valued order and stablity over experiments with increasing liberty. He died a constitutional monarchist who believed in liberty and justice, but also limitations to ensure stability.
Please let me know if you have further questions!