Investigators suspect French construction giant Bouygues was given a head start over other companies that were bidding for the work.
In May, Bouygues signed a contract with the government to build a massive new complex nicknamed the "French Pentagon" for the Defence Ministry. The complex is scheduled to be finished by 2014 and the state is to make annual payments of €100 to 150 million to Bouygues for 27 years.
Le Canard Enchaîné however alleges Bouygues was given the plans and specifications of the new complex before the other firms were allowed to work on them.
The Paris procecutor has opened an inquiry into corruption.
Defence Minister Gérard Longuet, who took office in February 2011, said he was unaware the new complex was being investigated.