I can’t see that log, the url appears to be truncated.
This is a weird one.
I assume your movie library in Jellyfin is targetted at the root? /media/Filme ?
I also assume you have your localisation set to french, have you tried temporarily setting it to us english and restarting the docker instance?
I’ve seen weird things happen if the docker instance starts before the mount, so if /data/Filme is a mount, it’s worth manually restarting your instance:
sudo docker restart jellyfin

Do you have nested libraries? Like a library pointed at /media and another one pointed at /media/Filme and maybe another at /media/Filme/Comedies ?
https://github.com/jellyfin/jellyfin/issues/8518

I’m pretty sure Firefox doesn’t know how to cast, that’s a chrome feature.
Secondly, a chromecast dongle can either be targetted locally by an app (such as chrome) or over the internet via https.
If you are just hosting on your windows laptop, you probably don’t have a domain with TLS, yes?
From localhost (the laptop itself), if you run chrome, you can probably cast to your dongle whilst on the same LAN.

If you have one of the newer Chromecasts with the remote, you can simply install the Jellyfin app on it directly, and address your Jellyfin install by IP and port.

Plex uses some fancy redirection work around these limitations, but it relies on an external service that they provide.

When you set up your libraries, it’s important that you point the path at the root folder, jellyfin expects a fairly specific naming convention.
Here’s how it is suggested to setup your tv shows for instance: https://jellyfin.org/docs/general/server/media/shows

Simplistically, lets say you have 2 shows called “Friends” and “The Witcher”, each with multiple seasons, and your NFS mount is /mnt/media.
You’d create something like: /mnt/media/tv
That’s where you’d point your tv library, at that “tv” directory. It doesn’t actually matter what the directory is called, but the library should be of type “shows”.
Under that /mnt/media/tv directory, you would create a directory for each show, and it would be the name of that show, so you’d get: /mnt/media/tv/Friends/ and /mnt/media/tv/The Witcher/
Then under those directories you would create seasons, to put your episodes in, ie /mnt/media/tv/The Witcher/Season 01/The Witcher - 01x01 - The End’s Beginning.avi
/mnt/media/tv/The Witcher/Season 01/The Witcher - 01x02 - Four Marks.avi

If you pointed the root of your library at /mnt/media/tv/The Witcher/Season 01/, it would probably fail to parse the episodes.
If you create your library as /mnt/media/allmystuff/ and just ram everything in there, it’s unlikely to find anything.
This may all seem a bit complicated, but there’s lots of tools that are useful to automate this process.
I personally recommend https://sonarr.tv/

If you are doing all of the above correctly, we’ll have to dig a bit deeper for more details.

As for “unsupported formats”, that most commonly happens when you have enabled hardware acceleration and it’s not working properly.
Whilst there’s several reasons why it may not be working, to rule it out, try temporarily disabling Hardware Acceleration under Dashboard -> Playback -> Transcoding.
The system should fall back to CPU transcoding which may be slow (hardware dependent), but at least it should function.

The Back to the Future trilogy is good for a re-view.

I was on a customer site with a laptop and no internet access.
I tried to use my preferred diff tool meld to compare the current configuration file with the backed up copy and meld just wouldn’t start…
Turns out an update of windows had decided it was evil and removed it since I’d last used it, silently as far as I am aware.
This is straight up evil as far as I’m concerned.

I am now inspired to search for a way to disable that though.

Not that I’m aware of.
The information would certainly be in the database, but I don’t know how to access it.

I mean yes, but that’s not a federation problem.

To completely strawman AND slippery slope what you’re saying:

As a car safety pro, who primarily deals with car crashes:

STOP

TOWING

TRAILERS

Agreed, dangerous, I don’t want numpties doing it.
But it’s a large part of why I have a car.

I want to be clear, that I disagree with his “federation is stupid” point, but email has problems right now.

Theoretically it’s federated, theoretically you can spin up your own mail server and self host.

But even if you do that absolutely perfectly (SPF, DKIM, DMARC etc), you can falsely end up on spam list, that effectively block delivery of your email to large segments of the network for days if not weeks.

Whilst theoretically federated, email falls under the broad dominion of google, microsoft and a couple of other large players.

Whilst you can override it manually, I heartily recommend modifying the folder/file names so that autodetection works correctly.

Otherwise you’ll end up just manually fixing it again next time there’s a significant library change.

Jellyfin doesn’t support this and is unlikely to add it, even as a plugin.

There are several tools out there that can automate converting a large library such as:
https://github.com/mdhiggins/sickbeard_mp4_automator
https://github.com/HaveAGitGat/Tdarr

And you can see a supported codec grid on here:
https://jellyfin.org/docs/general/clients/codec-support/

It seems like an mp4 file, with H264 video and ACC audio would be the safest bet, with transcoding only occuring when the client resolution is less than the native video resolution.

edit: This post doesn’t appear to have federated. As it contains links to tools which can perform the desired transcoding, I’m bumping it in the hope of it being sent.