By Peter Allen in Paris - The pair already face allegations that Miss Lagarde, the head of the International Monetary Fund (IMF), authorised a £270 million payout to a prominent supporter of the former French president when she was his finance minister.

Now, they face a separate inquiry in a row over the amount of compensation that Mr Sarkozy’s government should have paid following the collapse of Itea, an insurance company, in 2009.

Xavier Musca, a financial expert, is said to have recommended to Miss Lagarde that Maurice Nussenbaum, another expert, receive the Legion d’Honneur, France’s top civilian award, so he would rule in the government’s favour in the trade dispute.

Mr Nussenbaum later produced a report assessing the loss of Christian Laurent, who ran Itea, at zero, rather than the €400 million (£315 million) he claimed.

Anti-corruption police in Paris have launched a preliminary inquiry after Mr Laurent filed a complaint against Mr Musca, who went on to become Mr Sarkozy’s chief of staff. Mr Laurent also indicated that he will take legal action against Miss Lagarde, although the complaint will have to be sanctioned by a dedicated legal body dealing with allegations against former ministers.

Mr Musca, who is now a senior executive at the French bank Credit Agricole, denies any wrongdoing and has pledged to counter sue with a “false accusation” claim against Mr Laurent.

Miss Lagarde took over as head of the IMF a year ago from Dominique Strauss-Kahn.

The prospect of yet another IMF chief appearing in court was first raised last year when the Court of Justice of the Republic, a tribunal qualified to judge the conduct of French ministers, said Miss Lagarde may have been guilty of abuse.

Miss Lagarde is said to have allowed the equivalent of £270 million to be awarded to Bernard Tapie, a convicted football match fixer and tax dodger who supported her then governing UMP party.

Mr Tapie, the former head of Adidas in France, claims he was cheated out of millions by Credit Lyonnais bank when the sports kit empire was sold in 1993. In 2007, Miss Lagarde ended the long-running dispute by ordering a panel of judges to arbitrate and, in turn, they awarded Mr Tapie the damages.

Mr Sarkozy and Miss Lagarde deny any wrongdoing.