The Airbus A320 with 66 people on board disappeared from radar at 02:30 Cairo time (00:30 GMT), soon after leaving Greek airspace.
Greece’s defence minister says Flight MS804 made “sharp turns” and plunged before dropping off the radar.
A major search is under way in seas south of the Greek island of Karpathos.
Greek and Egyptian armed forces are involved in the effort, and France has offered to send boats and planes.
Mr Hollande said he was keeping an open mind about the cause of the crash.
“We will draw conclusions when we have the truth about what happened,” he said.
“Whether it was an accident, or whether it was – and it’s something that is on our minds – terrorism.”
There were 56 passengers – including three children – seven crew members and three security personnel on board. They included 30 Egyptians, 15 French citizens and a Briton.
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.
Aviation officials in Greece said earlier that air traffic controllers had spoken to the pilot a few minutes earlier and everything had appeared normal.
But Greece’s Defence Minister Panos Kammenos told a news conference that soon after entering Egyptian airspace, the plane had turned “90 degrees left and 360 degrees to the right” before plunging.
There was some earlier 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.
Some of the relatives of those on board gathered at airports in Cairo and Paris to wait for news.
Mr Hollande had earlier spoken to his Egyptian counterpart and both leaders were holding emergency meetings with their top officials, according to reports from both countries.
Flightradar24 listed details of the plane’s journey on Wednesday which showed it had flown from Asmara, in Eritrea, to Cairo, then on to Tunis, in Tunisia, before heading, via Cairo, to Paris.
Aviation analyst Alex Macheras told the BBC that Airbus A320s were regularly used for short-haul budget flights and had “an amazing safety record”.
In March, an EgyptAir plane was hijacked and diverted to Cyprus. The attacker later surrendered and all hostages were released.
A Freelance Journalist, Entrepreneur and Philanthropist. Editor-in-Chief of www.233times.com. A contributory writer for Ghanaian Chronicle Newspaper. An alumnus of Adisadel College where he read General Arts. He holds first degree in Bachelor of Arts from the University of Ghana; Political Science (major) and History (minor). He has also pursued MSc Corporate Social Responsibility (CSR) and Energy with Public Relations (PR) at the Robert Gordon University in the United Kingdom. He is a 2018 Mandela Washington Fellow (YALI) who studied at Clark Atlanta University on the Business and Entrepreneurship track. His mentors are Rupert Murdoch, Warren Buffet, Sam Jonah, Kwaku Sakyi Addo and Piers Morganview all posts by: Nana Kwesi Coomson
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