I am trying to figure out if a modern manufacture flintlock pistol in Europe requires a BATF form 6 for import, or whether it can be directly shipped to me?

When you find out, tell us...Geo

As long as it is a flinter or percussion gun no import permit is required. I am not sure what EU export rules are on the matter.
Steve

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!

I have recently imported percussion guns from England, South Africa and New Zealand.
All the guns were c.1840 to 1860. The shipping end understood US law better than our U.S. Customs and Border Protection folks. As Steve and Toby mentioned, no ATF Form 6 is required. Be sure that the shipper dates the gun on every form possible. Don't rely on the fact that it's a percussion or flint ignition system - Customs won't have any idea what those are.
There's a very helpful document on the Customs and Border Protection website - Requirements for importing new or antique firearms/ammunition.