That leaves us with: - reporting violations to the officials. They are chronically understaffed, have little technical expertise and it takes months to years for them to act. They are very hesitant to hand out fines, but theoretically can. - individual citizens suing a company to force them to abide by the law. This is rare because the citizen will have to cough up the money to go to court, and even if he wins, the company will only be forced to abide by the laws regarding this citizen, not in general. - publicly shaming companies into compliance.
A higher court might have different opinions, and I very much hope they will, because GDPR quickly becomes meaningless without enforcement.
Edit: I have literally no idea why this is downvoted. Unless it's just because you personally don't like me, please leave a comment explaining what is incorrect.
NOYB, the non-profit org founded by Max Schrems, has already been filing complaints with the French, Austrian, Belgian and German authorities: https://noyb.eu/
You can, but they will forward that to the applicable authority, which will be the local German one for German sites.
https://gdpr.eu/article-55-supervisory-authority-competence/ also states Each supervisory authority shall be competent for the performance of the tasks assigned to and the exercise of the powers conferred on it in accordance with this Regulation on the territory of its own Member State, and article 56 adds to that.