Armstrong has denied misbehaving during a test of his hair, urine and blood on March 17. No banned substances were found.
The agency, known as AFLD, said in a statement that the doctor leading the tests maintains Armstrong "did not respect the obligation to remain under the direct and permanent observation" of the tester.
At question is a 20-minute delay when Armstrong says the tester agreed to let him shower while the American rider's assistants checked the tester's credentials.
AFLD said cycling's governing body has given its permission to open disciplinary procedures against Armstrong, but did not say what the punishment could be.
AFLD president Pierre Bordry noted that the statement does not say that Armstrong is guilty of an infraction. AFLD is expected to make a decision on whether to proceed with sanctions after its nine-member ruling committee has considered the tester's report.
Messages left with Armstrong's spokesman for comment Thursday were not immediately returned.
Armstrong, who has had tense relations with France's anti-doping authorities for years, is hoping to win an eighth Tour title in July after having retired in 2005.
Bordry said the agency has not yet decided whether to seek sanctions against Armstrong. Asked if the agency is launching disciplinary proceedings, he said: "Not yet. We'll see."
Armstrong recently gave his own version of events, saying he wasn't sure of the identity of the drug tester.
"I did not try to evade or delay the testing process that day," Armstrong said in a statement Tuesday.
Armstrong was training in Beaulieu-sur-Mer in southern France when the test was conducted. Armstrong said he had returned from a ride to find the tester at his house, identifying himself as a representative of a French lab.
In France, drug testers take an oath before a court to discharge their duties honestly before they are allowed to work.