It depends on the law in question. Civil law typically requires that the plaintiff's cause of action and desired remedy be defined in the relevant code or statute. This doesn't mean the average person is powerless; every civil code I know of will let you file a lawsuit for breach of contract, for example. I have no knowledge at all of Spanish law, though, so I have no idea who has grounds to sue whom and under what code. If a similar situation happened the US, you'd probably file a lawsuit against Cloudflare, the ISPs, and the relevant sports league and sort it out in court.

You would do the same in a civil law country, sue the sports league and ISP. State that an "unlawful act" happened (blocking your service) and claim damages due to loss of traffic and the extra work it caused you.