The prosecutor's penalties, which also include a 100,000-euro fine as well as the prohibition from voting or holding a public office for five years, are similar to the ones pronounced two years ago in a first fraud trial that ended with Richard being cleared of any wrongdoing.
The prosecutor added that 24 months of the three-year prison sentence should be suspended.
The judges will hear the pleadings of Richard's lawyers and others from next week. No date has been set yet for the court's decision.
Richard has denied the allegations, saying he was doing his job and only played a secondary role in the arbitration process in which French tycoon Bernard Tapie was awarded 403 million euros ($491.62 million) in the state-funded settlement.
Tapie, 78, did not attend most of hearings of the appeals trial as he suffers from cancer.
The former businessman and minister of Socialist President Francois Mitterrand in the early 1990s is locked in a fight over the sale of his stake in sportswear firm Adidas in 1993 to Credit Lyonnais, then government-owned, and the compensation he won over the transaction 15 years later.
Richard is accused of complicity in the disputed payment. He was working as chief of staff to then-finance minister Christine Lagarde when it was made.
($1 = 0.8923 euro)
(Reporting by Mathieu Rosemain; editing by Jonathan Oatis)