Actually, EU countries have pretty high tariffs for some US exports, and other countries too, higher than US used to have until today.
That's how the common market remains competitive. We lower barriers for trade inside EU, while protecting our market from outside exports. Data is all available. Cars for example, US had tariff of 2.5%, EU 10%.
> Cars for example, US had tariff of 2.5%, EU 10%.
This is highly misleading:
Pickup trucks, which is a major share of the US car market, had an import tariff of 25% since 1964 (so it was pretty much the same average tariff level but with the EU doing less targetting).