I am going to start by saying yes, eink is an option if you want to connect to a Calibre web server and grab a book from your personal library. I do it all the time. The eink device needs to be able to connect to the internet (WiFi needs to be available), and the device have a web browser....which just about every device does these days. They might call it an “experimental” browser, but it still works to connect to Calibre web. Sometimes I have to say
http://mypublicipfor.my.Calibre.me:123456/mobile. (The /mobile is the important part) but it works fine.
Now that you know eink is a choice, for Europe / France... I’m not from there, but check out Pocketbook, and Onyx Boox. There is of course always Amazon Kindle too. But I think as a Calibre person you may like pocketbook or boox more.
I have tried a boox (a year + ago), and I have pocket book touch hd 3. I personally like the pocketbook over the boox, but everyone is different in needs and wants. Both make a device of about the same diagonal size as an iPad mini