HMS Vanguard and Le Triomphant were badly damaged in the crash in heavy seas earlier this month.
First Sea Lord Admiral Sir Jonathon Band said the submarines came into contact at low speed and no injuries were reported.
Both the UK and France insisted nuclear security had not been compromised.
The two submarines are key parts of each nation's nuclear deterrent, and would have been carrying missiles, though both the UK and France have insisted there was no danger of a nuclear incident.
"Now that this incident is public knowledge, the people of Britain, France and the rest of the world need to be reassured this can never happen again and that lessons are being learned."
Meanwhile, SNP Westminster leader Angus Robertson has called for a government statement.
"The Ministry of Defence needs to explain how it is possible for a submarine carrying weapons of mass destruction to collide with another submarine carrying weapons of mass destruction in the middle of the world's second-largest ocean," he said.
The Campaign for Nuclear Disarmament described the collision as "a nuclear nightmare of the highest order".
CND chair Kate Hudson said: "The collision of two submarines, both with nuclear reactors and nuclear weapons onboard, could have released vast amounts of radiation and scattered scores of nuclear warheads across the seabed." BBC news
HMS VANGUARD
Launched in 1992
One of four British submarines carrying Trident nuclear missiles
Displacement (submerged) 16,000 tonnes, 150m (492ft) long
Can carry 48 nuclear warheads on a maximum of 16 missiles
Full crew is 145, including 14 officers
Submerged speed of 25 knots
LE TRIOMPHANT
Launched in 1994
One of four French ballistic missile nuclear-powered subs
Displacement (submerged) 14,000 tonnes, 138m (452ft) long
Can carry 16 ballistic missiles with nuclear warheads
Full crew is 110, including 15 officers
Submerged speed over 25 knots
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