I know this answer must vary with geography but is there such a thing? If I remember my history lesson correctly europes history is littered with people coming from somewhere else and the only people I can think of not coming from outside Europe is the celts (the Basque?) and the Sapmi peoples.
Is european people from outside Europe?
Who are the indigenous people of Europe? It depends how far you want to go back.
If you go back longer than 40,000 years ago the indigenous people of Europe were Neanderthals who had interbred with Homo Sapiens. About then the Neanderthals went extinct in Europe and were succeeded by the undifferentiated Sapiens fresh out of Africa streaming in from the direction of the Near East and Asia. The genotype of these peoples suggests that they had black or dark brown skin, stringy dark hair, and blue eyes. These people were simple hunter-gathers. These seem to be the first Homo Sapiens in numbers in Europe.
Next, about 10,000 years ago, a second people entered Europe from Anatolia bringing farming with them. Farming spread throughout Europe but it varied how much these people mixed with the existing hunter gatherer population. It definitely was a population mixture rather than a population replacement.
The Anatolian genome survived virtually unchanged on the island of Sardinia. If you want to know what the Anatolian farmers looked like then google images of Sardinians.
The 10,000 year old Cheddar Man specimen from Somerset England is a example from this time period. Cheddar Man had pretty much the features of a hunter-gatherer: dark brown skin, dark hair and blue eyes. Remarkably, living relatives of Cheddar Man were found by DNA testing within 100 miles of the site where Chedder Man was found.
So if you want to tell Nigel Farage that the first Englishman had dark brown skin go ahead.
Finally, the Proto-Indo-European people swept in from the steppes north of the Caspian Sea riding horses, hauling wagons, kicking ass and taking names (actually they were giving names because these are the PIE after all) and they conquered all before them.
So, the indigenous European was a mixture of the genomes from the hunter-gathers, the Anatolian farmers and the Proto-Indo-European peoples with a pinch of Neanderthal thrown in.
Who We Are And How We Got Here, by David Reich