They have many questions to answer. How do they skirt the NPT? If they rely on the UK --which is not an EU country, or even if they rely on France, who makes the call, who has authority and what happens when some country tells France "launch" but France doesn't agree. Do those other countries have guys with the launch codes in assigned siloes?
You just don't ratify it, simple. The US does not ratify treaties all the time, especially now.
Coming under the French nuclear umbrella explicitly means that if a country is under extreme threat of nuclear attack, France will 100% retaliate. Unlike the current scenario where even if the country is an EU ally, France can still choose to refuse.
Later down the line, France could even choose to delegate nuclear hosting to those countries, like the US does with Turkey and the like. Obviously those nations don't get access to the codes.
At the end of the day, everything works on the basis of trust, and while the US has broken its covenant, the EU countries have not, especially not with each other.
Everyone else is breaking treaties left and right - who cares at this point?
"Withdrawal Clause: Countries may withdraw with three months' notice if "extraordinary events" jeopardize their supreme interests. " Doesn't seem that hard to leave it.