It is generally believed by people who study nuclear strategy that this in fact does not work.

Imagine Russia invades Poland. Will the UK Nuke Moscow? Probably not - because Russia would surely retaliate, on the UK!

Imagine Russia nukes Paris. Does the UK Nuke Moscow? Probably not! For the same reason.

As always, yes minister got it all right: https://youtu.be/3OpsP-gz_00?si=_uKmwkZUbE_fTNCM

I have read some experts views a while back and as far as I understood it’s more complicated. Suppose that Russia launches nukes for The Netherlands or South-West Germany, it’s likely that the UK/France will retaliate ‘just in case’ because it’s not immediately clear if the nukes are not destined for the UK/France.

But yeah, Poland/East Germany is probably too far away and there will be debates about nuclear sharing.

The European nuclear arsenal isn't for countering Russian invasion, it's for MAD. If Russia tried to invade poland, they get kicked out by Nato conventional forces instantly (and probably take Kalliningrad while they're at it). If, OTOH, France's nukes are to prevent Russia from using nukes.

There is no European nuclear arsenal. There is a French nuclear arsenal. It functions to deter other countries from using nuclear weapons against France.