Former officials are known to have been charged with a number of crimes, including fraud, including an episode in which Platini received two million Swiss francs (€ 1.887 million) from FIFA in 2011 for his work as an adviser between 1998 and 2002.
Both defendants have denied their guilt.
In 2015, the defendants received an eight-year disqualification from football and related activities, with Blater later reducing the sentence by two years.
As late as May 2015, Blater was elected for a fifth term, but only a few days later he announced his resignation as president. Blater spent 17 years as president of FIFA.
The trial in Bellincon will run until at least June 22, with a verdict scheduled for July 8.