The visit, designed to underscore historic ties and a burgeoning security relationship between America and its oldest ally, takes place as Hollande tries to shrug off speculation over his love life.
Obama met Hollande at the steps of a Boeing-757 version of his Air Force One jet at Andrews Air Force base, for a short flight into Virginia to visit Jefferson's beloved mansion at Monticello.
The visit was planned as a chance for Obama and Hollande, who speaks good English, to forge a personal relationship in highly symbolic surroundings.
The serious business will begin on Tuesday, with Oval Office talks likely to focus on the war in Syria, Iran's nuclear program, Ukraine's political crisis and security concerns in Africa.
Washington and Paris share a tough stance against Tehran and Damascus, and US forces provide intelligence and logistics support to the French operations in Mali and Central African Republic.
Hollande hopes to leave his split from long-time girlfriend Valérie Trierweiler behind, but her absence will be noted when he goes solo to Wednesday's state dinner in a plush marquee on the White House south lawn.
His trip is the first full state visit by a French leader since 1996 and is expected to highlight the "excellent working relationship" between the United States and France, according to sources at the Elysée.
But the pair will also discuss issues that have bedeviled relations, including concerns over mass US spying in France, and economic ties will also be on the agenda.
The leaders will hold a joint press conference at the White House after their discussions on Tuesday.
Jefferson, the third US president, served from 1801 to 1809 and was both one of the founding fathers of the United States and one of the country's first diplomats in Paris.