Edit: if you have a link of the video on the arte website, you might wanna try to copy the link and put it into yt-dlp. It is capable of downloading from youtube with sponsorblock information but also capable of downloading videos from other sites. For example the ARD Mediathek or Arte.
For a complete series its difficult. I guess you could copy all the links of each episode, put it in a .csv file, and let GPT write a script that opens up a Terminal/CMS/Powershell that calls yt-dlp with the parameter being the link of each episode.
Naming to be S01/E01 could get difficult but you could make another row in the .csv file and let GPT edit the script, so that after the download is complete the file gets renamed to the corresponding row.
Oooor you go the easiest way and sail the high seas, go to serienjunkies.org or other sites like this one, and go with one of the one-click-hosters, pay them and be good for a year or whatever time range you would choose.
Have you tried jDownloader? If normal link search doesn't work, try the deep search (or get into the websites source code and search for the media file and input that into jDownloader).
yt-dlp can download playlists and such. Have you tried using a link to some overview page or some such? Either way, how many videos can a series on arte have? 5 or 6? How that can be called tedious is beyond me.
Don’t know if it works for this but have you tried jdownloader 2? That’s what I use for most things. It can scrape pages and maintains a download queue
https://github.com/fnep/mtv_dl
mtv_dl allows searching the Mediathekview database from the command line and download all videos that haven't already been downloaded and that fit the search.
I use it to download new episodes from TV shows that I'm interested in