As far as I know, there are no spaceports in the European Union.
Why is it so?
The area of the European Continent is too far away from the equator and there are very few places allowing an eastward orbital launch over an ocean. Used first stages should not crash on densely populated ground.
But French Guiana, where the Guiana Space Centre is located, is one of five French overseas departments and a part of the European Union. Overseas departments are integral parts of France and the European Union, they are represented in the the European Parliament and use the euro as their currency.
There have been a lot of historic rocket launch sites in European mainland used for suborbital launches, see this Wikipedia list.
A new spaceport is planned in Scotland for orbital launches, the Sutherland spaceport. Launches over the ocean are possible in north to northeast direction, but not in south to southeast. But when it is finished, it will be no European Union spaceport (if there is no escape from Brexit).
There are currently suborbital spaceports.
Esrange in Sweden launches sounding rockets, including some up to 678 km. That's nearly 300 km higher than the International Space Station, so it is definitely possible to launch a payload into space from within the European part of the European Union. Esrange cannot yet launch into orbit, buth they plan to. Andøya Space Center also launches suborbital rockets, but it is in Norway and not in the EU (although it's pretty close to the EU politically and geographically).
The latitude is no fundamental objection, the most active spaceport in the world is at 63°N, so you can have spaceports at high latitudes. Low latitude is good for equatorial launches, high latitude is good for polar or retrograde launches. The reason there are no orbital launches from the European part of the EU is that (relatively) low-latitude sites in Europe are too busy and nobody has been willing yet to invest the necessary money at a high-latitude site, when European satellites can launch from French Guyana or Baikonur. The benefit of being within the EU and without crossing an ocean has so far not been considered worth the money.
Aha! But there is at least one spaceport in the European Union.
Namely Guiana Space Centre located in French Guiana – French overseas territory and hence part of the EU.
Technically not part of the EU, per se, but part of the EEC, Norway has launched a lot of rockets. Andøya Space Centre (formerly Andøya Rocket Range) has launched 1 200 rockets since 1962.
Mainly sounding rockets (scientific rockets with instruments measuring stuff in sub-orbital flight) have been launched, but on September 27 2018 they launched Europe's first hybrid rocket in more than 50 years to cross the Karman line, the Nammo Nucleus.