"It was a failure, the reasons will be determined by an investigation," said Lieutenant Commander Lionel Delort, a spokesman for the Atlantic Naval Prefecture.
He said the missile "self-destructed during its first propulsion phase... For an unknown reason."
The missile was test fired, without a nuclear warhead, from the Vigilant -- a strategic nuclear submarine -- from the Bay of Audierne at 0730 GMT and had been due to go down in the isolated north Atlantic.
The defence ministry said in a statement that it "was destroyed shortly after launch, over the ocean," without providing further details.
The M51, which has a range of 8,000 kilometres, was put into operation in 2010 following five successful test launches.