The New York Times summarizes an article on European Genetics from Current Biology which arrives the conclusion that it could very likely be possible to identify the nationality of Europeans by genetic testing.
Europe has been colonized three times in the distant past, always from the south. Some 45,000 years ago the first modern humans entered Europe from the south. The glaciers returned around 20,000 years ago and the second colonization occurred about 17,000 years ago by people returning from southern refuges. The third invasion was that of farmers bringing the new agricultural technology from the Near East around 10,000 years ago.
The pattern of genetic differences among present day Europeans probably reflects the impact of these three ancient migrations, Dr. Kayser said.
The map also identifies the existence of two genetic barriers within Europe. One is between the Finns (light blue, upper right) and other Europeans. It arose because the Finnish population was at one time very small and then expanded, bearing the atypical genetics of its few founders.
The other is between Italians (yellow, bottom center) and the rest. This may reflect the role of the Alps in impeding free flow of people between Italy and the rest of Europe.
Correlation between Genetic and Geographic Structure in Europe article