The 57-year-old insists he will give back the money he took if he is accused of illegally receiving unemployment allowance while working as a television pundit
According to AFP on Monday, a judge in Toulouse charged the newly-appointed boss with claiming illegal financial support after he was sacked by Nantes in 2009.
It is reported Baup did not declare that he was working as a pundit for French television channel Canal+ and continued to receive the allowance, with his wife also reportedly involved in the fraud.
Questioned about the charges, Baup told AFP: "There was nothing intentional. I followed the advice of professionals in these matters.
"If a mistake was made, there will not be a problem for me to return the money."
Baup, who guided Bordeaux to the Ligue 1 title in 1999, took charge of Marseille earlier in the month following Didier Deschamps' resignation.