The Airbus A320 disappeared from radar at 02:30 Cairo time (00:30 GMT), soon after leaving Greek airspace.
There were 66 people on the plane in total, including three children, seven crew members, and three security personnel on board Flight MS804, EgyptAir said.
Mr Hollande said all information confirmed that the plane had crashed.
A major search and rescue operation is under way in the Mediterranean Sea, involving the Greek and Egyptian armed forces. France has offered to send boats and planes to help in the effort.
Both French and Egyptian officials have refused to comment on what brought down the plane.
Although there is no evidence yet to indicate a terrorist attack, the possibility is not being ruled out.
Subscribe to our newsletter and stay updated on the latest news and updates from around the Muslim world!
It was only seven months ago that a Russian passenger jet was brought down over the Sinai by ISIS, which has vowed to target the Sisi regime of Egypt.
The 66 passengers included 30 Egyptians, 15 French citizens, 2 Iraqis, and one Briton, Canadian, Belgian, Kuwaiti, Saudi, Algerian, Sudanese, Portuguese and Chadian citizen.
Timeline
Flight MS804 left Charles de Gaulle airport in Paris at 23:09 local time on Wednesday (21:09 GMT) and was scheduled to arrive in the Egyptian capital soon after 03:15 local time on Thursday.
EgyptAir said the plane had been flying at 11,300m (37,000ft) when it disappeared from radar shortly after entering Egyptian airspace.
Greek aviation officials said its air traffic controllers had spoken to the pilot a few minutes earlier and everything had appeared normal.
One official told AFP news agency the plane had crashed “around 130 nautical miles” off the southern Greek island of Karpathos.
There was some confusion over whether a distress signal had been sent by the plane.
Egypt’s state-run newspaper al-Ahram quoted an EgyptAir statement as saying the Egyptian army’s rescue and search had received a distress call from the plane at 04:26 local time – which would be around two hours after the flight disappeared.
But Egypt’s military subsequently said that no such signal had been received.
