Air France flight AF447 plunged into the Atlantic during a storm on June 1, 2009, after the plane's Pitot tubes – which enable pilots to monitor their speed – malfunctioned
The sources said the magistrates had ordered that manslaughter charges be brought against both Airbus and Air France be dropped.
The main association of victims' families called the decision an “insult to the memory of the victims” and announced plans to appeal.
The crash was the worst in Air France's history and prompted much soul-searching about pilot training after it emerged that one of the co-pilots reacted incorrectly when the plane stalled after the speed sensors froze over
It took two years to find the wreckage of the Airbus A330, which was eventually located by remote-controlled submarines at a depth of 3,900 metres.
Magistrates later charged Air France and Airbus with manslaughter, but prosecutors in July recommended that only the airline face trial.
The prosecutors accused Air France of negligence for failing to train its pilots about how to react if the Pitot tubes malfunctioned, after several incidents involving the sensors in the months leading up to the crash.
In such cases the magistrates leading the investigation have the final say over prosecutors, but the decision can be appealed by defence or civil plaintiffs.
Since the disaster, pilot training on dealing with unforeseen circumstances has been stepped up in France and several other countries.
Aircraft safety has been in the spotlight this year after two crashes involving the 737 MAX plane from US aircraft manufacturer Boeing, which has led to the global fleet of the aircraft being grounded as a result.