The Airbus A-330, carrying 216 passengers and 12 crew members, had been due to land at Charles de Gaulle airport in Paris at 09:10 GMT.
Estelle Youssouffa, Al Jazeera's correspondent in Paris, said authorities at Charles de Gaulle had said that there was "no hope" for the airliner.
"It seems to have simply vanished from radar screen. President Sarkozy has expressed his great concern and asked his government to put all its efforts into finding the missing plane," she said.
The Brazilian air force said the aircraft was far out over the the sea when it went missing.
Jean-Louis Borloo, the French environment minister, said there were "powerful" tropical storms in the zone.
"It is the kind of jet made to handle this kind of circumstance but there must have been a build-up of circumstances," he said.
Air force jets have taken off from the Brazilian island of Fernando de Noronha, about 340km off the coast of the country, to look for the missing aircraft.
Gabriel Elizondo, Al Jazeera's correspondent in Sao Paulo, said the island is very close to where authorities last had radio contact with the airliner.
"There's definitely an urgency here and the Brazilian head of the military has sent out a statement saying he's going to be working very closely with the French authorities to scramble any resources necessary until this plane is found," he said.
Three naval ships are also participating in the search operation.
There are reports that in addition to French and Brazilian passengers on board the airliner, there were some Italians and Britons.
John Guntrip, a former crash investigator, said the aircraft's disappearance indicated a "catastrophic failure".
|The Airbus A-330 has a good track record, with only one other crash on record [AFP]
"It would a be a catastrophic failure because there would be various automatic devices that would be activated by the crew that would help to locate the aircraft.
"But the fact that they are searching for it shows that it didn't report its first mid-Atlantic reporting point by radio by satellite phone which means it never got there," he said.
Jim Morris, an aviation expert and former pilot for the the UK's Royal Air Force, told Al Jazeera that while modern aircraft are "designed to withstand a lightning strike", an electrical storm could still cause damage.
"It can cause structural damage such as burning through and blowing out rivets and it can potentially cause electro-magnetic interference with the flight control systems," he said.
Authorities have set up a crisis centre at Charles de Gaulle airport and Dominique de Bussereau, the French junior transport minister, is on his way to the scene.
In a statement, Airbus said the missing airliner had been delivered to Air France from the production line in April 2005.
The company said the the aircraft, which was powered by CF6-80E1 engines, had accumulated approximately 18,800 flight hours in some 2,500 flights.
The Airbus A-330 family of aircraft has a good safety record.
Its first, and last crash, was on June 30, 1994, when an A-330 crashed on a test flight shortly after takeoff from Toulouse in France, killing all seven on board.