The source, who is not authorised to speak publicly, said that Hirt had failed the test in Rouen, western France, on Aug. 3 before he travelled to London.
Hirt was knocked out of the 5,000 metres after finishing 11th in his first-round heat on Wednesday.
The International Olympic Committee said it was unaware of the case. There was no immediate comment from the IAAF, the world governing body for athletics.
Hirt is the second French runner to fail a test for EPO this summer after 3,000 metres steeplechase specialist Nour-Eddine Gezzar was suspended in the build-up to the Olympics.