The missile carried no nuclear weapon for the test flight, which was closely monitored by specialists at a test center in Biscarosse, in southwest France, as well as by the Monge missile-tracking ship, ministry spokesman Jean-Francois Bureau said.
The M51 is designed to replace the M45 submarine-launched ballistic missile, or SLBM.
The M51 can carry six TN-75 thermonuclear warheads and has a range of up to 6,000 miles.
Defense Minister Michele Alliot-Marie "expressed her great satisfaction" at the success of the test, her ministry said.
Alliot-Marie insisted on the "need to conduct tests to verify the performance of future missiles of the strategic ocean forces, and attain an important stage in the adaptation and modernization of our dissuasive force."
Greenpeace activist Xavier Renou called the test a violation of France's commitments to nonproliferation and a provocation to the international community.
Bureau insisted the test conformed to all of France's international commitments, including the Nuclear Nonproliferation Treaty.
The missile is made by EADS Space Transportation in a $3.8 billion project.