As a French, I've been exposed since childhood to the official propaganda about how our "Force de Frappe" protected us from the Warsaw pact.
I'll be curious to know if our nuclear arsenal was taken seriously by the USSR, and how it was perceived by the US.
Were we effectively capable to inflict sufficient damage to the USSR to have an impact on their plans regarding western Europe?
I'll be interested about official/public reactions at the time and more confidential reports made public after the fall of the USSR.
The French and British weapons in large part existed and continue to exist to increase national standing in the world. Being a nuclear power is a fairly exclusive club and the members of this club have a bigger stick when dealing on the world stage.
France's strategy was in large part to act as a trigger for US weapons. France during the 50's was not convinced of US dedication to defense of Western Europe. This was only exacerbated by the Suez crises in 1956 and again increased through the 60's and 70's as France withdrew from NATO and Soviet technology increased allowing the Soviet Union to strike US cities with nuclear weapons. France wanted to ensure that if The Soviet Union invaded Western Europe the US would be forced to intervene.
During the 1960's the French strategy was that if an invasion of French territory was imminent French Bombers would perform a Nuclear strike against all cities they could reach (Khrushchev was Ukrainian and most cities in the Soviet Union were beyond the reach of French bombers so Ukrainian cities were a major target) The Soviet Union would be forced to retaliate against France or accept huge losses with no response (in Soviet Doctrine this would signal they were unwilling to retaliate and would result in the US launching a preemptive strike.) The Soviet use of nuclear weapons would trigger the US to use nuclear weapons. Basically France found a way to put their own finger on the trigger of US nuclear weapons.
Both the US and the USSR knew that France had the ability to trigger mutually assured destruction. So absolutely the French Nuclear ability was taken very seriously. For a fraction of the cost of US and Soviet arsenals France had an effective nuclear deterrent.
1981 paper about nuclear proliferation