Sources at the French foreign ministry told the paper that the charismatic former minister returned to the diplomatic service -- which he left in 1993 -- in September in order to receive the pay-off, equivalent to $138,500.
The British paper said it was unclear exactly what entitled Villepin to the payment and that "the exact details are shrouded in a French bureaucratic device called the 'career termination mechanism'."
The sources added that the move was likely approved by Foreign Minister Laurent Fabius.
According to the Daily Telegraph, officials are angry at the pay-off, which comes amid President Francois Hollande's unpopular austerity drive.
A spokesman for Villepin told paper there had been an "administrative error which Mr Villepin has already asked to be rectified by the relevant authorities as soon as it was noticed", but did not explain what that error was, or whether the money had been returned.
A ministry spokesman added there had been "no discretionary or preferential treatment" for Villepin, who served as prime minister from 2005 until 2007 under the leadership of Jaques Chirac.