I've seen Fedora being widely recommended among the Linux distros. Sadly, there are many problems that come with Fedora. A lot of this information might be a bit hard to find so I wanted to put everything I found in one place.
- Fedora is (kind of) owned by Red Hat (IBM).
Red Hat sponsors Fedora. They own and pay for the infrastructure used for all the Fedora-related things. They own the Fedora trademark and logo. Big decisions are made by the FESCo. While the committee itself is elected by Fedora community, they're pretty much just exclusively Red Hat employees (for F41 elections all 5 of elected candidates work at Red Hat). I'm not going to talk about what-ifs much here, but if there would ever be a divide between what RH wants and what community wants, you can see it being an issue.
- US laws and Fedora
Fedora has to follow the US law. In practice, we have seen what that means a while ago, when they had to remove support from some multimedia codecs due to the US patent laws. Since then, basic functionalities like video playback in a web browser/video player have been broken, so for example you can't play Twitch videos "by default" in Fedora, since the codecs are missing (youtube works as they use av1). To circumvent it, you either have to use third party repos or flatpak.
- Fedora Export Control Policy and it's consequences
https://docs.fedoraproject.org/en-US/legal/export/ Yet another US law that Fedora has to adhere to. Basically, if you live in a country that the USA treats as an enemy, you should not use Fedora. This is yet another one that was actually applied in real life and resulted in basically kicking out a longtime contributor because he had the misfortune of being born in the wrong country. You can read all about in on that person's blogpost:
https://ahmadhaghighi.com/blog/2021/us-restricted-free-software/
Free and open source software are made collaboratively by communities on the internet, its difficult to determine any nationality for many projects. Trying to run a fully EU linux system is impossible. But as most free software itself is not a revenue generating business, so largely use what you want.
But if your goal is a more European system I do have a few reccomendations.
OpenSuse: Its a free to use version of an enterprise distro, similar in business model to red hat/fedora but it is based in Germany.
Linux Mint: This is generally my pick for a beginner friendly distro. The project lead and founder is French.
KDE: Is my choice of desktop environment. It is German. The lead developer is German, and the nonprofit that funds the development is headquartered in Berlin. There are many pieces of software under the KDE umbrella including the Calligra office suite, and the Krita image editor.
I also recommend Blender, the 3D animation package. It is primarily Dutch, as the founder and nonprofit foundation behind it are based in the Amsterdam.
But really use what you want and works best for you. Nearly all free software projects, including all I've listed are some sort of international amalgam.
The best way to make free software more European is to be European and contribute. Volunteer, write code, write documentation, help users in community, report bugs, donate, fork, maintain or release something you made freely.