In most European countries I have traveled to during the past months the popular opinion regarding the US is that we have to operate under the worst-case-assumption that the US won't assist or would even actively use their tech as leverage in the case of a conflict.
That was unthinkable a year ago, but it is now. Given that it is probably better to roll your own in the mid/long term and not rely overly on US tech.
I think it's very simple. France hinted at placing its own nuclear bombers closer to the Russian border. That does not require that other European countries trust France. It's just France shifting its nuclear posture a bit more to the East.
Does France have submarines with nuclear weapons? I’m not sure how much of a deterrent nuclear bombers are compared to ICBMs, but it’s better than not having them.
My understanding is that jetfighters with nuclear weapons are meant to deliver an ultimate warning by nuking the invading army. ICBM are what comes next (unless the enemy went ICBM first).
That being said this all assumed that Russia had a strong air-defence. The various strikes that Ukraine has been able to make on Russian territory seems to have challenged that idea. I don't know how confident Putin feels he could block such attack, so that adds to the dissuasion too. The thing with nukes is that it only takes one missile to go through.
Though technically France always worked on that assumption. Or rather, that the US would support France against a soviet invasion up to a certain level, but wouldn't risk a nuclear war for France's pretty eyes. Hence the will to have no other finger than the French president's finger on its red button.
And to be honest that's the only way it can ever be. I don't understand France's talk about extending its nuclear deterence to the rest of Europe. Those european countries can no more rely on France than France can rely on the US in those extreme scenarios. Nuclear deterence is like the bee's sting. It will die if it uses it, but it's because you know it will use it that you tread carefully.