18 Brumaire occurred a mere month before Washington's death. This matters for several reasons, the first being that while Washington would have had a general awareness of the Revolution, and Napoleon as prominent military figure as he had already attained notable status from early campaigns like Egypt, he of course could leave us no record of his thoughts on most of the better known parts of Napoleon's career, including his ascent to power, so insight would be limited. Second though, the timing of his death gives us a wonderfully insightful look at the reverse though, and Napoleon's thoughts about Washington, which we'll focus on.
Washington was absolutely an international celebrity of his day, and he represented more importantly what David Bell terms the "charismatic revolutionary hero", and this was an image that Napoleon actively sought to cultivate as well, and used the the symbolism of Washington, and the American Revolution to do it. Word reaching France of Washington's death a few months after his coup and his elevation to First Consul, Napoleon used the occasion to make a grand gesture of solidarity to the revolutionary principles that Washington had fought for and represented in international minds, ordering an official period of mourning lasted for ten days, and a massive ceremony in his honor where the keynote speaker, poet Louis de Fontanes, made sure to include numerous references to the similarities between the two men and emphasize that Napoleon was carrying on the legacy of Washington. This all happening at a time when, France and the United States were in a de facto state of war!
This was not the only gesture, even if it was the most grandiose. In portraiture, no one is more famous for the 'hand-in-jacket' than Napoleon, but Washington did it before him in a famous portrait by Charles Willson Peale done in 1776, picturing the General in his militia uniform in the early days of his Revolutionary campaigning. It is a pose that predates Washington too, one associated with being a good leader, but there is decent speculation that it was Washington's portrait in particular that may have influenced Napoleon's choice, although he never made it explicit. More concretely, coming from Napoleon's own words and others, we know that a small statue of Washington was kept in personal collection of his along with other notable patriots and great statesmen's figures, outside of public-eyes.
Of course, the cynical among us, not to mention those with hindsight, would find it to be more darkly humorous than anything, as Napoleon had come to power through a coup, and would go on to crown himself emperor, while Washington was elected, and is remembered as someone who refused unlimited power and prefered to live up to his reputation as the "American Cincinnatus", but that is less important here, for us, than the image that he projected and that Napoleon wished to revel in and use for his own justifications of power. Washington was an incredibly powerful symbol, the cult surrounding him one which even predated the French Revolution and had been present in the last stages of the ancien régime, brought back by the French officers who had served in the Revolution had returned full of praise for the American general, and to which the young Napoleon from the first days of his military career. Well before Napoleon, praise of Washington was on the lips of the revolutionaries, and thus it was a model Napoleon was well aware of, and consciously worked to make use of for his own ends.
At the end of the day, of course, ge was decidedly not the French Washington, but he certainly wanted to make it look like he was, and this stretched back years into his military career, reflecting an appreciation for Washington, as well as other leaders who fit a similar mold, most prominently probably being Pascal Paoli, a Corsican patriot who Napoleon had idolized in his younger days. So this shouldn't be intended to push things too far over and say Napoleon literally modeled his career on George's. It was one of many influences which he drew on when needed, and it was an influence which was hardly restricted to Napoleon alone among those involved in the Revolution.
To be sure, in the end Napoleon wasn't completely blind to the irony. Later, trapped on St. Helena, he reminisced about his desire to be a Washington, although at least with the self-awareness to recognize that he needed to be a "crowned Washington" and needing a "universal dictatorship". Perhaps attempting to self-justify his actions while holding them up to the ideal he had once claimed, he nevertheless stated his belief that it was necessary to be taken as an equal in the "congress of kings" that characterized Europe, and of which the United States lacked at its own doorstep.
Now looking to the reverse, again, it is harder. Napoleon has Washington's whole career to draw on, while Washington had only the beginning of the latter. We certainly can say he knew of the man. Napoleon made the news for his doings as a military leader, before being First Consul, and his actions even directly impacted Washington's life. When the Marquis de Lafayette was imprisoned by the Revolutionary government, his son Georges, in America stayed with the Washingtons, and was there when word reached Mt Vernon that "General Bonaparte had sued for the liberation of the Marquis" in 1797. More broadly, Washington was quite wary of the French Revolution and its military successes... in no small part due to Napoleon's military acumen, but unfortunately I do have things to do today! So while I think I have done just treatment to one half of the question, I'll leave the other half to someone else to jump into, as American perspectives on the French Revolution is really a whole new topic to dive into, and my own small anecdote there can hardly do it justice.
Sources
Abbott, John Stevens Cabot. Napoleon at St. Helena: Or, Interesting Anecdotes and Remarkable Conversations of the Emperor During the Five and a Half Years of His Captivity. Harper, 1871.
Bell, David A. “Charismatic Authority in Revolutionary and Napoleonic France.” In Rethinking the Age of Revolutions. Oxford University Press, 2018.
Bourrienne, Louis Antoine Fauvelet de. Memoirs of Napoleon Bonaparte: To which are Added an Account of the Important Events of the Hundred Days, of Napoleon's Surrender to the English, and of His Residence and Death at St. Helena. Merrill and Baker, 1891.
Horn, Jonathan. Washington's End: The Final Years and Forgotten Struggle. Scribner, 2020.
Roberts, Andrew. Napoleon: A Life. Penguin Publishing Group, 2014.
Zall, Paul M., ed. Washington on Washington. Lexington, Kentucky: University Press of Kentucky, 2003.