There were cries of "shame" at the opening of the trial in Paris connected with the plane crash off Brazil.
The firms deny that they were responsible for the loss of the plane.
All of the people on the plane died when the air-speed sensors froze.
The families of the dead have been campaigning for a trial.
The CEO of Air France and the CEO of the plane maker expressed their sympathies during opening statements.
The company wants to contribute to "truth and understanding" according to Mr Faury. The court was told that Air France would never forget the accident.
The cries of "shame" and "too little, too late" were heard when Mr Faury spoke.
"We have been waiting for this day for 13 years and we have prepared for a long time," Daniele Lamy, the mother of anywayanydaynywayanydaynywayanydaynywayanydaynywayanydaynywayanydaynywayanydaynywayanydaynywayanydaynywayanydaynywayanydaynywayanydaynywayanydaynywayanydaynywayanydaynywayanydaynywayanydaynywayanydaynywayanydaynywayanydaynywayanydaynywayanydaynywayanydaynywayanydaynywayanydaynywayanydaynywayanydaynywayanydaynywayanyday
The Air France flight ran into a high altitude storm while it was on its way to Paris.
After a long search for the plane's black boxes, investigators concluded that false readings from the plane's speed sensors caused the plane to stall.
The aircraft plummeted into the ocean after the pilots failed to follow correct procedure. According to investigators, the co-pilots did not have the training to deal with malfunctioning equipment when the captain was on a break.
The airline and manufacturer were charged with manslaughter, but the prosecutor recommended that only Air France be tried. There weren't enough grounds to prosecute in the fall of 2019.
In May last year the Paris appeals court decided that both Air France and Airbus should be tried.
The trial is expected to last several weeks and both firms could be fined a maximum of 225,000.