POD Treaty of Mortefontaine: signed September 3, 1800 ending hostilities between France and the United States of America(three weeks early). The news travels across the Atlantic just in time to sway public opinion towards Adams for the admirable way he upheld the nations honor and avoid a potentially destructive at the same time, it is enough to swing 200 voters in New York City.
Adams takes New York state in the general election. However that isn't enough to guarantee Adams the Presidency. A contingency election must be held in the House of Representatives and the Senate. The lame duck House is still controlled by the Federalists, and they have no qualms about reelecting Adams since he did get carry the majority of states.
Adams will; however, have to contend with a Congress completely hostile to him. His veto pen still has power, though only if he keeps his party united behind him. So does Adams veto attempts to downsize the Navy (he can expect some help from South Carolinian and Maryland Republicans on that).
Any other thoughts on what Adams might or might not do differently, able or otherwise.