Ummmm, OK. France's lone aircraft carrier is a sometimes-sea-going reliability problem. They have 3 amphibious assault ships and 14 frigates (only five of which are general purpose; the rest are air protection or anti-submarine). French SSBMs and SSNs seem so specialized as to be marginally useful. The German navy has 3 general purpose frigates, 2 of which will soon be retired, plus some that are specialized, and 6 diesel-electric attack submarines (SSKs) which seem marginally useful. Italy actually has a couple of light carriers (Harriers and/or F-35s), a mix of 17 destroyers and frigates of general and specialized purpose, and 8 small SSKs that are basically anti-shipping or anti-submarine (like the French and German SSNs and SSKs).
EU countries' navies are very obviously sized and purposed with the idea that the USN will range the oceans and EU naval forces will be defending smaller areas and be mostly specialized purpose. There are no equivalents to USN Arleigh Burke DDGs, Ticonderoga class CGs, Los Angeles, Seawolf, and Virginia class SSNs (attack submarines), or Nimitz class CVNs. Italian amphibious assault ships are only capable of carrying helicopters, not equivalent to the USN's Wasp class, which can carry Harriers or F-35s as well as helicopters.
Pretty much any large sized and/or sustained effort against Iran will be dependent on US participation.
Frankly, I think Iran is playing a game of geopolitical chicken, betting that Russia will make the US and Europeans very reluctant to act meaningfully. And betting that the American and European public will not support meaningful action.