The bodies of 24 people have been recovered from the site in the Atlantic Ocean where Air France flight 447 went down en route between Rio de Janeiro and Paris on June 1.
The plane disappeared from radar screens after flying into turbulence.
Investigators have said there were "inconsistencies" with the speed readings prior to the crash, raising speculation that speed sensors on the aircraft, known as pitot tubes, may have iced up, feeding wrong information to the cockpit and confusing the pilots as they hit a storm.
Air France said at the weekend it was speeding up the replacement of the speed sensors on all its Airbus long-haul planes, but did not give any timeframe for the modifications.
On its website, Alter advised pilots to "refuse any flight on a A330/A340 which have not modified at least two pitot sensors".
It was not immediately clear whether Air France pilots would heed the union's advice or whether this would have any effect on the company's operations.
The French air accident agency has said it is too early to pinpoint a possible cause.
Finatti said that despite its statements the union was "not trying to replace the official investigation which is going to take a long time".
The search for the plane's "black box" flight recorders received a boost on Monday after Brazilian navy divers recovered the tail fin of the Airbus A330 jet, where the recorders are located.
The union's comments came as a helicopter bearing some of the 24 bodies so far recovered from the site of the crash, arrived at the Brazilian island of Fernando de Noronha.
|French investigators will examine the plane's components [AFP]
Officials said that bodies and debris picked up from the ocean waters off the coast of Brazil, would be transferred to the mainland coastal city of Recife.
Investigators hope to identify the remains by DNA provided by families, fingerprints, medical records, tattoos and other clues.
Interpol, the global police agency, has also said it will help French and Brazilian officials identify the victims.
Ronald Noble, Interpol secretary general, said: "Since the victims of this tragedy came from all parts of the world, international collaboration will be essential in ensuring their accurate, dignified and speedy recovery and identification so as to enable the families to begin the healing process."
A statement from the agency said an Interpol officer would be attached to the French gendarmerie unit from Paris charged with identifying the victims.
French investigators will also examine the plane's components.