Daily newspaper Le Monde reported that an internal memo seen by AFP said the aircraft "was missing a third of its screws on part of the aircraft's body."
The A340 had just undergone a routine maintenance check in China at Taeco-Taikoo Aircraft Engineering Co., which it left on November 10th.
The aircraft spent three days at Paris' Roissy airport but the missing screws were not noticed until several days later in Boston.
The area concerned was a protective panel between the fuselage and the wing which serves to reduce drag by smoothing out the edges.
The newspaper reported that a spokesperson for the airline confirmed the incident and that an internal inquiry had been launched.
The same spokesperson insisted that "at no point was the security of the flight" in question. He added that the aircraft was only grounded "for a few hours."
The internal memo seen by AFP joked that the A340's check-up in China had "as always, exceeded our expectations!"
Taeco is a world leader in aircraft maintenance and works for airlines including Lufthansa, British Airways and American Airlines.