Apparently, like most Americans of the Founding era, he vigorously supported it (though obviously not its excesses). France was a key ally of America's in the Revolutionary War and their Revolution, at the time, was viewed by most as an extension of the American Revolution. "Liberty, Equality & Fraternity" were viewed as American as apple pie. Jefferson, in France at the time, helped write their Declaration of the Rights of Man, which, intuitively, contained ideas strikingly similar to those in America's Declaration of Independence. In short: In the ideal, both the American and French Revolutions were based on the same Enlightenment principles. And traditional orthodox Christians supported the principles or ideals of both revolutions (though obviously such Christians did not or would not have approved of how the French ended up treating traditional Christianity). Further, a key player in the Revolution, Marquis de Lafayette, was one of George Washington's closest friends.
Right now when composing this post, I've yet to read the following article from JSTOR entitled George Washington and the French Revolution. I can't access it for free from home but will do so the next day I go in to work (I'm still working every day though; I'm a college prof; it's the summer and I'm teaching online courses until the Summer B session).
Rather, I've just stumbled upon a letter George Washington wrote to the French Minister January 1, 1796, what I'm basing my claim on. I'm going to reproduce it in whole and then comment on it:
Born, Sir, in a land of liberty; having early learned its value; having engaged in a perilous conflict to defend it; having, in a word, devoted the best years of my life to secure its permanent establishment in my own country; my anxious recollections, my sympathetic feelings, and my best wishes are irresistibly excited, whensoever, in any country, I see an oppressed nation unfurl the banners of Freedom. But above all, the events of the French Revolution have produced the deepest solicitude, as well as the highest admiration. To call your nation brave, were to pronounce but common praise. Wonderful people! Ages to come will read with astonishment the history of your brilliant exploits! I rejoice, that the period of your toils and of your immense sacrifices, is approaching. I rejoice that the interesting revolutionary movements of so many years have issued in the formation of a constitution designed to give permanency to the great object for which you have contended. I rejoice that liberty, which you have so long embraced with enthusiasm, liberty, of which you have been the invincible defenders, now finds an asylum in the bosom of a regularly organized government; a government, which, being formed to secure the happiness of the French people, corresponds with the ardent wishes of my heart, while it gratifies the pride of every citizen of the United States, by its resemblance to their own. On these glorious events, accept, Sir, my sincere congratulations.
In delivering to you these sentiments, I express not my own feelings only, but those of my fellow citizens, in relation to the commencement, the progress, and the issue of the French revolution: and they will cordially join with me in purest wishes to the Supreme Being, that the citizens of our sister republic, our magnanimous allies, may soon enjoy in peace, that liberty which they have purchased at so great a price, and all the happiness which liberty can bestow.
I receive Sir, with lively sensibility, the symbol of the triumphs and of the enfranchisement of your nation, the colours of France, which you have now presented to the United States. The transaction will be announced to Congress; and the colours will be deposited with the archives of the United States, which are at once the evidences and the memorials of their freedom and independence. May these be perpetual! and may the friendship of the two republics be commensurate with their existence.
This letter clearly shows how Americans viewed the French Revolution as a continuation of the American: Sister republics founded on "liberty." One thing that strikes me about this letter is its date: January 1, 1796. By that time the French Revolution had gone seriously haywire and they had already terribly mistreated Washington's dear Lafayette.
One pattern I've noticed with Washington (frustration for those of us trying to determine his exact opinions on things) is that he constantly tries to be all things to all people and has kind words to say for all sorts of various incompatible religious and philosophical systems. Except of course, for British Toryism. And notice his use of the term "Supreme Being" was exactly as the French referred to God in all three [one, two, & three] of their Declarations of the Rights of Man, another pattern of Washington's -- using the same "God-words" that the recipients of his correspondence used. Except, when speaking to orthodox Trinitarian Christians, with whom he often corresponded and to whom he was quite friendly and approving, he never spoke in Trinitarian terms, but rather used generic God words.