Pierre Razoux, a former defence official, said Paris refused to hand “the keys to the safe” to a rival in the arms race. The missiles used by Argentine forces killed 46 British troops during the 1982 conflict.
HMS Sheffield and Atlantic Conveyor were sunk, while HMS Glamorgan survived a strike.
British officials believe such a switch would have been in place to prevent the missiles being used on French forces.
Mr Razoux said the French had a defeat device that could “kill” an incoming missile, but Francois Mitterrand, the then president, would not share it with Margaret Thatcher’s government.
He said: “To my knowledge, this kill process… was only activated when the missile received a message from the target itself.
“Just like boats from the Royal Navy, French ships in a war zone had a series of electronic countermeasures that emit signals to neutralise missiles that we could have sold and could be used against us.
“It is an object – a type of box – that emits a signal on a particular frequency with particular data. It’s as if you had a whistle or a flute.
“Each one has a different sound and frequency. Without the right emitter you cannot neutralise, but to hand this over is like giving the keys to your safe to your neighbour. It’s not done.”
The Royal Navy’s only defence against the missiles was strips of metal fired from under the ships and decoys trailed by helicopters.
Mr Razoux said France had given the British “part of the technical details” of the Exocets along with intelligence about the Argentine weapons stockpile.
Asked why the French government had stopped short of giving Britain the ability to “kill” Exocets, he said: “It is because we were and still are competitors in the arms industry and Francois Mitterrand knew that if he had handed over the plans in full then the British would have let it be known the world over.
“That would have been very bad publicity for the French arms industry at a time when the French and British industries were competing fiercely in a certain number of key markets.”
Bob Seely, a Conservative a member of the Commons Foreign Affairs Committee, said: “It now seems clear that the French could have done more to help, and that is pretty disappointing if true because we would undoubtedly have saved British lives.
“All the more reason why the French should now be transparent about what happened.”
Simon Weston, 60, an ex-Welsh Guardsman who was badly burned in the bombing of logistics ship Sir Galahad in the conflict, said: “If they did do a dirty on the Sheffield, shame on the French.”
He said he “would be very, very disappointed”.