Platini and former Fifa counterpart Sepp Blatter were last year barred from the sport after being found guilty of ethics breaches over a $2m (£1.3m) "disloyal payment" between the pair.
Both men, who deny wrongdoing, had the bans upheld but cut from eight years. Platini, 60, wants the verdict annulled.
A decision could come early next week.
The three-member Cas panel judges the former France player`s case afresh and has the option of imposing a life ban for corruption.
Fifa`s ethics and appeal committees ruled there was "not sufficient evidence" to establish the payment was a bribe but said both men demonstrated an "abusive execution" of their positions.
Blatter, 80, is likely to attend the hearing to give evidence about the Fifa payment he approved for Platini in 2011 as backdated, uncontracted salary.
Blatter`s appeal against his six-year ban will be heard at a later date.
Gianni Infantino has succeeded Blatter as Fifa president, while Uefa has named Angel Maria Villar as acting president.