[jonathanstrange]

There is: https://edps.europa.eu/data-protection/our-role-supervisor/c...

There is also an online dispute resolution center: https://ec.europa.eu/consumers/odr/

This allows you to complain about a European company if you deal with it from another EU country.

[Kbelicius]

The first one isn't what you think it is. It is, AFAIK, only for complaints against EU institutions. For everything else (national, local, private and non profit entities) you need to contact the relevant national data protection authority