There's a couple things to consider when trying to playback videos in MC for Linux.
1) Depending on the site (arte.tv in this case) it may actively block embedded web browsers from streaming content and/or it uses DRM. I believe in MC for Linux generally, this is true for Netflix and Amazon, as the embedded Chromium it uses doesn't work with those sites if I recall correctly. MC for Windows it should work with those sites, as it uses the embedded Microsoft Edge (WebView2) for those sites. At least it should work until if/when Netflix/Amazon/etc. decides to block WebView2 from working this way.
2) While YouTube should work cross platform in MC, Google actively blocks all embedded web browsers from logging into those sites (so you have to stream without a logged in account). If arte.tv requires logins and they block embedded browsers, this may be an issue.
3) If you stream video (e.g. YouTube) through MC on Linux, do know that sound will not go through MC's engine on Linux or macOS. Only MC for Windows has the WDM driver, allowing audio to be routed through MC.
Ultimately, you're probably going to have to end up trying it yourself and seeing if arte.tv works. I've never even heard of the site, so your mileage may vary here. And also know if it does work, it may work for now, there's no guarantees that a site won't just up and block embedded web browsers from access.
