Unless there's a trade treaty stating this, then the US is not beholden to EU rules. Even if there is a treaty, they generally all give the US the ability to ignore their provisions if it is an issue of national security, and it's under that claim that the current administration has issued tariffs already.
Say the US applies a tariff on wine imports from France. What happens next? Does every other EU member in solidarity start self-applying the same tariff to their wines and sending that over to the US tax service?