The airline made the discovery in mid-November and said the screws were missing from a protective panel of an A340 plane after a full service by the Chinese company.
Taeco, based in Xiamen, southeast China, is one of the top service companies for long-haul planes and its other customers include British Airways, American Airlines, JAL, Emirates and Lufthansa.
"We have stopped sending our planes for the moment" to Taeco, Air France CEO Alexandre de Juniac said in Beijing.
Air France made the move as it awaits the results of its investigation, which is expected to take "a few days".
On Tuesday the Chinese firm announced it was launching its own probe.
Taeco has serviced Air France's Boeing 747 planes for over four years, representing "10 percent of our long-haul fleet", Juniac said.
The incident involved the second A340 plane sent to Xiamen for a full service.
A full service occurs every six years and takes just over a month, costing "several million dollars", an Air France official said.
Taeco services "between five and seven planes per year" for Air France, Juniac said. In an earlier statement, the number had been put at "less than five a year".
An Air France Boeing 747-400 was grounded in 2010 following a full service in China after some of the plane's surfaces were repainted using potentially flammable paint. The plane had been in the skies for over three weeks.