The firms deny involuntary manslaughter following the loss of the Airbus A330 flying from Rio de Janeiro to Paris.
The BBC reports relatives shouted protests at Air France chief executive Anne Rigail and Airbus boss Guillaume Faury as they expressed condolences during opening statements.
The investigation into the crash, which took several years, found speed sensors on the plane had given false readings during unusual weather conditions, causing the aircraft to stall.
In the ensuing four minutes and 24 seconds, the stall warning sounded 75 times, but pilots failed to follow correct procedure and lost control of the aircraft, which plunged 38,000ft into the ocean.
The captain was on a break when problems began and investigators concluded co-pilots did not have training to deal with the situation.
Airbus blames pilot error for the crash while Air France claims confusing alarms caused the pilots to react wrongly.
Both firms risk a maximum fine of only €225,000 in a trial expected to last several weeks.
