A judge had made the request because efforts to get them through "political channels" had failed, the lawyer said.
France, the former colonial power, has not yet commented on the request.
Mr Sankara's widow and supporters have repeatedly accused France of masterminding his 1987 killing because he was a Marxist revolutionary.
He was killed by soldiers in a hail of bullets shortly before a meeting of his cabinet in Burkina Faso's capital, Ouagadougou.
Mr Sankara's assassination led to his second-in-command, Blaise Compaore, seizing power in a coup.
Mr Compaore steered Burkina Faso into a strong alliance with France, which retains close political, security and economic ties with many of its former colonies in Africa.
Burkina Faso opened an investigation into the killing after he was ousted from power in 2014.
Speaking at a press conference in Ouagadougou, the family lawyer, Benewende Stanislas Sankara, said an investigating judge had formally asked French authorities to declassify military documents to see whether France had played a role in the assassination.
A request had also been made to interview French officials who were involved in Burkina Faso's affairs at the time, the lawyer added.
Burkina Faso issued an arrest warrant for Mr Compaore in 2015, accusing him of involvement in Mr Sankara's killing.
He has repeatedly denied the allegation, but has refused to return to Burkina Faso to stand trial.
Mr Compaore is exiled in Ivory Coast, also a former French colony.
Burkina Faso has asked France to declassify military documents about the killing of ex-president Thomas Sankara, a lawyer for his family has said.