Can't speak for other EU countries but the UK would require an export licence supported by a US Form 6. Since the application of the EU regulation known as PL9010 in the UK, the anti arms proliferation regulations have required an import permission to get the export licence.
This was designed to stop the export of surplus military arms to non-government forces in areas of conflict.
Where the ATF will not issue a Form 6 (eg pre-1899 guns) the UK export authorities will issue an export licence once this is explained to them.
Whether other EU countries follow this pragmatic approach, I have no idea. They may decide the matter is black and white or they may not even be aware of the rules!
