Prosecutors have recommended that Diack, who was president of the International Association of Athletics Federations (IAAF) from 1999 to 2015, be tried for corruption and money laundering.
The prosecutors want five other people, including Diack's son Papa Massata Diack, a former marketing consultant to the IAAF, to stand trial.
Lamine Diack, from Senegal, has been questioned by prosecutors in France on several occasions. But his son, who like his father lives in Senegal, has refused to cooperate.
Investigating magistrate Renaud Van Ruymbeke must now decide whether the case should go to trial.
The French investigation began in 2015 when Britain's Sebastian Coe took over from Diack as IAAF president.
The backdrop to the investigation is the alleged system of state-sponsored doping uncovered in Russia by the World Anti-Doping Agency (WADA).
Prosecutors allege that Lamine Diack, now aged 85, was prepared to accept funding for political campaigns in Senegal in return for lenient treatment by IAAF anti-doping officials of Russian athletes.
Also in the prosecutors' sights is Diack's former advisor, Habib Cisse, and the IAAF's former anti-doping chief Gabriel Dolle. They recommend both men should be charged with "passive corruption".
In 2017, Papa Massata Diack branded the corruption allegations against himself as "a witch hunt" and accused France of having "taken hostage" his father.
The IAAF suspended Russia in November 2015 after the allegation of state involvement in doping emerged.
Russia was allowed back into the Olympic fold last year but the IAAF continues to ban Russian athletes from competing under their own flag.