The aircraft had undergone routine maintenance in China, before flying to Paris and then on to the US before the potentially disastrous blunder was finally spotted.
Air France problem was revealed in an internal union document leaked to French news agency AFP.
The company have blamed aircraft mechanics in the Chinese city of Xiamen, were the airline’s jets are often serviced because of lower costs.
An Air France technical operations spokesman said: “The plane flew for several days before it was grounded because one third of the screws holding down a piece of bodywork were missing.
“It was part of the outer covering of the wing and at no point was flight safety compromised.
“The maintenance team that works for Air France are internationally recognized and this is the first ever incident of its kind.”
But an aircraft construction expert said: “The piece itself may not have endangered the flight if it came off.
“But there is always the risk that it could have struck and damaged another very important part of the aircraft as it became detached and blew away in flight.”
An Air France union spokesman described the oversight as “deplorable”.
The spokesman added: “Pieces of an aircraft should never simply go missing during maintenance. It is not the first time this has happened either.
“Last year a Boeing 747 was grounded after undergoing maintenance in China because parts of the plane had been painted with flammable paint.”
The crash of an Air France Concorde 11 years ago, killing 113 people, was blamed on a strip of metal on the runway which punctured the plane’s tyres and sent rubber fragments flying into a fuel tank.
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