According to the families' petition the investigation should "define penal responsibilities" in the crash because, they say, Air France ignored "indications of diverse failures" in the aircraft's controls.
Nelson Faria Marinho, the head of the association representing the families, said the investigation into the crash, conducted by France's bureau of accident investigations – the BEA - was implemented with no input from the Brazilians.
|Search teams have called off a hunt for the plane's two flight recorders [AFP]
"We are asking the Brazilian authorities to follow this investigation and open a criminal process because a crime has been committed," he told local media.
Flight 447 crashed during stormy weather in an area of the Atlantic ocean around 1,450km off northeastern Brazil.
No emergency communications were received from the aircraft and an extensive sea search failed to recover the aircraft's "black box" voice and data recorders.
A French oceanographic ship "Pourquoi Pas", which had been leading the search for the recorders, was expected in Senegal on Thursday after calling off final efforts to locate and retrieve the recorders.
French investigators have said they will gather an international team of experts to continue the investigations into the cause of the crash, although they have given no further details.