"It is a catastrophe the likes of which Air France has never seen," Nicolas Sarkozy said after meeting relatives and friends of passengers at a crisis centre at Charles de Gaulle airport.
Earlier, Air France chief executive Pierre-Henri Gourgeon told reporters: "We are without a doubt faced with an air disaster."
He added: "The entire company is thinking of the families and shares their pain."
Flight AF 447 left Rio at 1900 local time (2200 GMT) on Sunday. It had 216 passengers and 12 crew on board, including three pilots. The passengers included one infant, seven children, 82 women and 126 men.
Air France confirmed that there had been 61 French and 58 Brazilians on board.
Among the other passengers were 26 Germans, nine Chinese, nine Italians, six Swiss, five Britons, five Lebanese, four Hungarians, three Irish, three Norwegians and three Slovaks.
Lightning theory doubts
The Airbus 330-200 had been expected to arrive in Paris at 1110 local time (0910 GMT).
Tom Symonds, BBC News transport correspondent
The Airbus A330 airliner is likely to have begun its journey tracking the coast of Brazil northwards before striking out across the Atlantic. A few hundred miles from the shore, radar coverage peters out - from there on, crews use high frequency radio to report their position.
The Brazilian Air Force says the plane left radar screens near the islands of Fernando de Noronha, 230 miles from the coast. The firmest clue to its fate comes from the data message sent via a satellite network at 0214 GMT reporting electrical and pressurisation problems. This suggests whatever happened, happened before the crew could put out a mayday radio call. It was likely a sudden and catastrophic emergency. Even a double engine failure at cruising altitude would normally give the crew around half an hour's gliding time.
Air France says the plane may have been struck by lightning, but this rarely results in tragedy. More likely lightning damaged electrical systems, possibly leading indirectly to the plane's ditching.
Although passengers survived a landing on the Hudson River in New York in January - it is rarely successful, especially in the middle of an ocean the size of the Atlantic.
It made its last radio contact with Brazilian air traffic controllers at 0133 GMT (2233 Brazilian time) when it was 565km (360m) off Brazil's north-eastern coast, Brazil's air force said.
The crew said they were planning to enter Senegalese airspace at 0220 GMT and that the plane was flying normally at an altitude of 10,670m (35,000ft).
At about 0200 GMT, the captain reported entering heavy turbulence caused by Atlantic storms, French media report.
At 0220, when Brazilian air traffic controllers saw the plane had not made its required radio call from Senegalese airspace, air traffic control in the Senegalese capital was contacted.
At 0530 GMT, Brazil's air force launched a search-and-rescue mission, sending out a coast guard patrol plane and a specialised air force rescue aircraft.
France is despatching three search planes based in Dakar, Senegal, and has asked the US to help with satellite technology.
"The plane might have been struck by lightning - it's a possibility," Francois Brousse, head of communications at Air France, told reporters in Paris.
David Gleave, from Aviation Safety Investigations, told the BBC that planes were routinely struck by lightning, and the cause of the crash remained a mystery.
Missing man Arthur Coakley’s wife, Patricia, and his business partner Ken Pearce
"Aeroplanes get hit by lightning on quite a routine basis without generally any problems occurring at all," he told BBC Radio Five Live.
"Whether it's related to this electrical storm and the electrical failure on the aeroplane, or whether it's another reason, we have to find the aeroplane first."
France's minister responsible for transportation, Jean-Louis Borloo, ruled out hijacking as a cause of the plane's loss.
Mr Sarkozy said he had met "a mother who lost her son, a fiancee who lost her future husband".
Flight AF 447 left Rio at 1900 local time (2200 GMT) on Sunday
Airbus A330-200 carrying 216 passengers and at least 12 crew
Contact lost 0130 GMT
Missed scheduled landing at 1110 local time (0910 GMT) in Paris
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