The 57-year-old, who took over as the Ligue 1 side's coach earlier this month as Didier Deschamps quit and joined France, is accused of having received benefits while he was working for French television channel Canal+ after he was sacked by Nantes in 2009.
A judge from Toulouse, where Baup was living before moving to Marseille, laid the charges in June but the news was only made public on Tuesday.
Baup, who led Bordeaux to the French league title in 1999, said he would happily return the money.
"I had no intention to fraud," he told a news conference at Marseille's training facility La Commanderie.
"This is the reality. I trusted some law experts and advisors who led me into this... I am willing to pay some damages, even to give the whole money back. I'll do whatever it takes."
Marseille, who reached the Champions League quarter-finals last season but had a poor Ligue 1 campaign, travel to Turkish side Eskisehirspor for their Europa League preliminary third round first leg on Thursday.