The former head of the International Association of Athletics Federations (IAAF) was in the dock following a four-year investigation by the French financial prosecutor's office.
The 87-year-old from Senegal, who ran the IAAF between 1999 and 2015, is also accused of giving and receiving bribes. He denies the charges.
Prosecutors claim that Diack obtained around one million euros of Russian funds to help back Macky Sall's campaign for the 2012 Senegal presidential election in exchange for the IAAF's anti-doping arm to cover up or delay offences by 23 Russians.
The aim was to allow the Russian athletes to compete in the 2012 London Olympics and the 2013 world athletics championships in Moscow.
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Two other men Habib Cissé and Gabriel Dollé also went on trial with Diack.
Cissé, Diack's former legal advisor, is said to have received hundreds of thousands of euros acting as a go-between for the IAAF and Russian athletics authorities.
Dollé, the former IAAF anti-doping chief, is accused of receiving bribes amounting to 190,000 euros.
Diack’s son, Papa Massata Diack, is also accused of money laundering, giving bribes and aiding the receiving of bribes.
However, he is absent from the hearing after managing to elude French authorities despite two international arrest warrants. Diack junior has remained in Senegal where authorities say they will not extradite him to France.
Two other defendants are also missing. Valentin Balakhnichev, a former head of the Russian athletics federation and IAAF treasurer, is accused of giving and receiving bribes and aggravated money-laundering.
Alexei Melnikov, formerly Russia's chief distance running coach, is accused of receiving bribes.
Sebastian Coe took over from Lamine Diack as president of the IAAF in 2015. The organisation was renamed World Athletics amid a plethora of reforms including the introduction of more women to the upper echelons of the organisation. Presidents were also forbidden to serve for more than 12 years.
The hearing in Paris is expected to last for six days.
