Without the American "umbrella": is Europe capable of creating its own nuclear arsenal?

It is difficult to imagine a hypothetical European deterrence that would not involve the involvement of British and French nuclear arsenals, even given that the British deterrent is technologically dependent on the United States. The development of any other European state's nuclear programs would violate its obligations under the Treaty on the Non-Proliferation of Nuclear Weapons and could increase the likelihood of a Russian attack. It is much easier to destroy an embryonic nuclear program than a fully formed one."