Socialist Hollande, who was making his first visit to Britain since he was elected in May and was also meeting the queen for the first time, spent around half an hour alone with the 86-year-old monarch.
Just two photographers -- one British, one French -- were allowed in at the beginning of the meeting to record it for posterity.
Hollande and the queen, who was wearing a yellow dress, shook hands cordially, before she presented him with two gifts -- framed and signed portraits of herself and her husband Prince Philip.
In return, the president gave the sovereign, a keen horse rider despite her age, a Sevres porcelain statue of Amphitryon, the wife of Greek sea god Poseidon, on the back of a sea horse, by the artist Antoine Orlandini.
"The queen gave him a very warm welcome," a spokesman for the French presidency said.
"She said she had had good relations with successive French heads of state and followed French politics closely."
Prime Minister David Cameron had earlier said that Hollande would be taking part in the very British ritual of teatime when he met the sovereign.
"I know that the president has an engagement of a cup of tea with her majesty the queen," Cameron said as he wrapped up a joint press conference with Hollande at Downing Street in central London.