Perhaps I may elucidate.
Firstly, NATO article 5 does not require any allied nation to provide any military response to an attack on another. Under the terms of the article a stiff diplomatic note to the attacker would suffice, and perhaps a stern ticking off at the UN. [1]
The fear being, under the present administration, that is all that would be given in the event of a Russian attack on, say, the Baltic states etc.
The American "nuclear umbrella" is therefore somewhat thin and cannot be relied upon.
The next point brings me to a discussion of NATO history and the transition from the policy of "Tripwire" to Flexible Response".
In the early days of NATO, when the USA was the sole nuclear power, and even when Russia had just a few warheads, and each side had only IRBMs (Thor, Cuban Missile Crisis and all that), the policy was "Tripwire". Any attack on NATO would automatically be responded to to with a nuclear response. All well and good.
However, once the threat grew and, with ICBMs and SSBNs, the USA would then be at threat if an exchange took place, substantial doubt grew as to whether such a policy was credible - well covered in Yes Prime Minister" [2].
As a result NATO moved to a policy of "Flexible Response" and nuclear coupling. Any attack would be met by an increasingly strong response from the battlefield to the strategic level. But these levels of response would all contain nuclear weapons where, at the lower levels, use was delegated to the brigade etc. Hence nuclear mines, Honest John, Pershing, WE177 etc. [3]
THe idea being that, since use would escalate, and since neither Washington or Moscow had total control, the risk of escalation to a full scale exchange was such that no one would risk an attack at all.
That policy lasted up the deployment of GLCMs to Greeham Common etc and the end of the Cold War since when, gradually, all have been withdrawn except a handful of US B61 freefall bombs - under total US presidential control - in countries not directly at threat, Germany, Italy, Netherlands, Turkey and the UK. [4]
How does the French Nuclear Deterrence scheme improve on the above?
Firstly, on the strategic level, it provides a nuclear guarantee apart from the US umbrella, and not one under NATO control where use could be vetoed at the Military Committee level by the USA. That does not assure it's use (I have no idea of the actual guarantees in the signed treaties and and doubt they will ever be published), but it adds significantly to the risk Russia would have to take and consider.
Secondly, on the tactical level, it involves France deploying FAF elements of their
Force de Dissuasion [5] to 9 partners including 4 under direct threat - Denmark, Poland, Norway and Sweden, bringing back the policy of nuclear coupling with a possible theatre tactical use escalating to a strategic level - drawing in the USA. [6]
[1]
https://cepa.org/article/willfully-v...0aAq4lEALw_wcB
[2]
[3]
https://www.academia.edu/126475709/D...n_the_Cold_War
https://christophbluth.substack.com/...ctical-nuclear
[4]
https://en.wikipedia.org/wiki/B61_nu...omb#Deployment
[5]
https://en.wikipedia.org/wiki/Force_de_dissuasion
[6]
https://www.france24.com/en/europe/2...clear-umbrella