President Obama's rare out-of-town trip with a foreign leader opened two days of events marking Mr Hollande's state visit to the US.
The French leader is travelling without a female companion, following his very public split with First Lady Valerie Trierweiler after claims he had an affair.
The absence of a companion created a tricky situation for US officials planning a high-profile event where diplomatic protocol and etiquette are in the spotlight.
The White House is carefully avoiding any mention of Hollande's personal drama and has a grand welcome reserved only for America's closest allies.
Standing together in Monticello's grand foyer, Mr Obama said the elegant home represented "the incredible bond and the incredible gifts that France gave us".
The two leaders arrived in Charlottesville, Virginia, after a short flight on Air Force One from Washington.
Travelling together in Mr Obama's armoured limousine, the presidential motorcade then wound its way through the rolling hills towards the white and brick mansion.