There has been more than one migration of Homo sapiens to Europe and they all left some of their DNA. The first was around 20-25KYA (when the Neanderthals still lived there) and we know very little about their origin since their DNA has been greatly diluted by subsequent migrants.
The migrations that get the most attention because they gave rise to most of the modern European nations were the Indo-European tribes: first the Celts, then the Germanic people, then the Greeks, with the Romans somehow sneaking in there (some scholars think they are an offshoot of the Celts), and finally during historical times the Albanians and the Slavic peoples.
But the European gene pool has many other contributors. The three pre-Indo-European peoples we can name are the Etruscans who arguably built the first civilization in Europe but are now extinct, the Basques who are still hanging on in the Pyrenees, and the now-thriving Finnic peoples including the Estonians and the Sami (or "Lapps"). We have plenty of evidence of the other earlier inhabitants whose names have been forgotten, some of it as sturdy and massive as Stonehenge, other bits as small as arrowheads. And of course their DNA is mixed with that of the people who displaced them with the superior technologies they brought from western Asia, where the Agricultural Revolution was in full swing and civilizations had already begun springing up.
Migrations of non-Indo-European peoples have also taken place subsequently to the establishment of Indo-European culture in Europe. The Huns came from Asia, as did the Magyars who now inhabit their country; the Magyars are related to the Finns and they may all be Mongolic peoples. The Bulgars adopted a Slavic language but they are also an Eastern people whose origin is something of a mystery. The Ottomans of course are descendants of the Mongols, and the Jews are a Semitic people.
This adds plenty of spice to the European gene pool, and migration patterns can easily account for different mixes in different parts of the continent.