‘Thomas Jefferson Wins The 1796 Election’.
And thus, succeeds Washington as the 2nd President instead of the 3rd (after John Adams IOTL).
First of all, I'm going to assume that we're looking here at a "Jeffersonian revolution, but four years earlier" scenario. Which implies that Jefferson also picks up a Congressional majority. This suggests that the Federalists get embroiled in something the public finds objectionable. Since a lot of the public antipathy stemmed from opposition to the more hard-line Federalist legislation of the Adams administration, let's assume that certain correspondence of the more avid Federalists is leaked and published. This would alter the public to the fact that a disturbing number of leading Federalists was not only open to, but actively in favour of, various repressive measures.
The Democratic-Republicans profit, and Jefferson sails into office four years early.
Adams, as per his statements at the time, will decline to serve as VP, and will instead retire to his home state. Adams would be additionally motivated by the fact that he wasn't a very rabid Federalists, so he'd feel that the Hamiltonians have screwed him over during the elections.
This leaves Jefferson facing exactly those Hamiltonians, and he can easily portray them as closet monarchists and benighred Tories who would imitate every vice of Parliament that the Americans had objected to in the first place. (And in certain cases, this would be a pretty accurate charge, in fact!)
Anyway, what of his policies?
Jefferson was, if nothing else, a radical proponent of free speech. AS President, he referenced the deluge of literal death threats he got from irate Federalists as sure evidence that he lived in a free country. This was a man whose conception of free speech etruly encompassed ALL speech, no exceptions. As such:
definitely no Alien and Sedition Acts. The POD I suggested may easily see Jefferson pushing for more legislation, further bolsering free speech. The result may be, if Jefferson really gets his way, that concepts such as "libel" and "slander" are wholly excised from the law, and America really becomes the land where you can see
anything you want.
There would be no complete saturation of the judiciary with Federalists. Jefferson would appoint his own Democratic-Republicans all over the place. Marshall would never be Chief Justice, and there would be no
Marbury v. Madison. As such, no judicial review. Congress and Congress alone would be allowed to determine whether any law was Constitutionally sound. The Supreme Court would 'merely' be the Court of final appeal, but OTL its influence on the legitimacy of certain laws would be absent. The would be no Judicial Act of 1801. Instead, Jefferson would push for legislation hemming in the power of the Judiciary, to avoid judges from becoming too powerful.
Jefferson was pro-France. By the time of his election, Robespierre and the Convention and Committee of Public Safety would have been removed. Jefferson would point to the much more moderate Directory as evidence that after a turbulent revolution, matters soon calm down again. All's well that ends well. There would be no quasi-war, and Jefferson would push for trade with France. This would benefit both parties, allowing American produce to meet French demand, while French money would stabilise the American economy.
This may have just enough effect to help the Directory assert its legitimacy, thus averting Napoleon's coup. (Or at least delay any such coup.)
On the American side, it would remove the basis of the Federalist argument that America sorely needs to borrow money from Britain. The Federalists would be further discredited. Jefferson, noted opponent of public debt, would almost certainly try to pass legislation to ban public debt. He may not succeed, but I think he can get his proposal through in which the amount of debt is strictly limited, and all debt must be paid back within 20 years.
Jefferson was acutely aware of the strategic and economic importance of New Orleans, and would try to buy it from Spain. (It had been ceded by France to Spain in the secret treaty of Fontainebleau in 1762, which was revealed to the world in 1764.) As in OTL, he'd initialy desire to by only New Orleans and environs. The Spanish, unlike Napoleon, wouldn't be automatically inclined to push for the purchase of all of the vast Louisiana Country. It might be possible for Jefferson to effect a different purchase, such as New Orleans alone, or New Orleans and Florida. I do think that with French backing, he'd be able to get a deal realised. He may even get Congress to sign off on it, avoiding his OTL contradiction of his own principles (in agreeing to the purchase without prior Congressional say-so).
Generally speaking, trade will be booming, tariffs will be low, and there will be no subsidies for domestic industry and such things. America is very small-government, and primarily agrarian.
Meanwhile, the Federalists are a fading power. The South loves the export of its produce, so the Southern Federalist faction wholly evaporates. Only in the North-East, where they rely on good trade relations with Britain, do the Federalists cling on for a while as a regional faction.