The case was centered around a USD 2 million payment from FIFA to Michel Platini with Sepp Blatter's approval in 2011.
The trial is set to last 11 days and the three federal judges hearing the case are scheduled to deliver their verdict on July 8.
Sepp Blatter is due to be questioned Wednesday and Michel Platini one day later. Both are expected to give closing statements on June 22.
Nasser Al-Khelaifi was cleared again of a charge of incitement to commit criminal mismanagement for allowing Jerome Valcke to use a vacation home.
Once the most powerful man in the world of football, Sepp Blatter is facing charges of defrauding FIFA in a Swiss criminal court.
The criminal complaint was said to be filed on Nov. 17, two weeks after Michel Platini was indicted along with former FIFA boss Sepp Blatter on fraud charges.
Former FIFA president Sepp Blatter and vice-president Michel Platini have been accused of fraud. The verdicts are expected on July 8.