Matomo

Matomo is an open source web analytics service. You can install it on your own server, which means the visitor data of your website stays in the infrastructure you control instead of being sent to an analytics company. It also covers tag management and session recording.

The company behind Matomo is based in New Zealand, so the product itself is not European. Because it is open source and self-hosted, though, you can run it on a server in the EU and use it as a European alternative to American analytics tools. That makes it a good match for organisations with GDPR obligations and their own hosting.