Cloud storage and file sync from European companies, as alternatives to Google Drive and Dropbox, from Tresorit and pCloud to Nextcloud, which you can run on your own servers.
Yes. PixelUnion, Yungle, Fenritec Alpha, Internxt, Tresorit, Twake Workplace, Jottacloud, Proton Drive and 2 more (see the table) are free or have a free plan, according to the pricing each company publishes. Free plans usually carry limits; each product page links to the company's terms.
Which European cloud storage tools are open source?
zeitkapsl, Nextcloud, Internxt, Proton Drive and Filen publish their source code under an open-source licence. Each product page shows the licence and where the code is.
Which European cloud storage tools can you host yourself?
Fenritec Alpha, Nextcloud and Twake Workplace can be run on your own servers, according to their own documentation.