If the US rhetoric continues it will not be long until you will see some currently non-nuclear EU countries start talking about contingency options. It will take a while, but it is good to remember that the reason there are so few nuclear weapons states is not because it is terribly hard, but because states have abstained for the global good and benefit of non-proliferation. This with the implied protection from states that have it.
If that no longer holds, then we enter a new era where non-proliferation will be history.
I think already at this point, that there will be several more nuclear states in Europe (inside EU) in the not so distant future.
Many of the countries already have certified delivery platforms, or have ordered them.
Of course, we're treading in new waters and it's completely unknown if any existing contracts and treaties will be honoured anymore, but that concern will be secondary to this, I think.
I say it is a secondary concern because 1. basically any European nation can put together a delivery system, ballistic or cruising, should they have to; and 2. creating the weapon itself is not really that big of an undertaking for a modern high-technology nation state level actor.
My bet is that we will see Poland to become the next nuclear weapons state. Possibly in collaboration with some neighbours around the Baltic Sea. Who knows, maybe Ukraine joins