"The site has been disrupted all day," a ministry of defence spokesman told AFP, adding that they suspected a "denial of service" attack where a system is flooded with information in an effort to clog it up.
The site was not breached and there were no security concerns, the ministry stressed. An inquiry has been launched.
The Anonymous group said it has launched the attack to "avenge" the death of Remi Fraisse, a 21-year-old protester who died during violent clashes over a controversial dam project in southwestern France.
Investigations into the case suggest he may have been killed by a police concussion grenade.
"For too long, Anonymous has lain stagnant. We have not taken action. But, now, we will. We will protest the killing of this young man," the activists said in a statement.
"Today, we take action against the inhuman things done to Remi and other protesters around the world," they added.
Fraisse's death in the protest — the first such tragedy in mainland France in nearly three decades — caused an outcry in the country and embarrassed the government, which was accused of not reacting quickly enough.
Local authorities subsequently decided to suspend work on the dam, though they have not scrapped it indefinitely.