The seven-times Tour de France champion “did not respect the obligation to stay under (the) direct and permanent observation” of the tester, the AFLD said in a statement.
The 37-year-old American, who returned to the sport in January after 3 1/2 years retirement, denied any wrongdoing on Tuesday.
Armstrong was asked to provide urine, blood and hair samples when returning from a training ride around Beaulieu-sur-Mer last month.
“In a letter sent to the Agency on April 8, UCI (International Cycling Union) president Pat McQuaid said an interpretation of the World Anti-Doping code and UCI anti-doping rules confers the AFLD the right to open a disciplinary procedure against Lance Armstrong,” the statement read.
“The AFLD is competent to impose disciplinary sanctions to people who do not hold a French licence but train on the national territory.”
Any sanction imposed on Armstrong would be valid on French territory only.
Armstrong is set to ride the Tour de France, which starts in Monaco on July 4.
In a statement on Tuesday, Armstrong explained: “We told the tester we wanted to check with the UCI to confirm who he was and to make sure he wasn’t just some French guy with a backpack and some equipment to take my blood and urine.
“Johan (Bruyneel, Astana team manager) stayed with him and in his presence called the UCI to find out what was going on.