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Human rights have to do with things like torture, unfair detention, having a fair trial, etc...

You are not going there because an hosting company shutdown your mail service.

Last cases for reference: https://hudoc.echr.coe.int/eng#{%22languageisocode%22:[%22EN...}

Actually, a hosting company challenging the police in jurisdiction where ECHR is ratified would go exactly there once it exhausts options in local courts. But not a customer of a hosting company challenging the decision of a hosting company.

.. on what basis? (a) you've not checked whether the OVH user agreement allows this kind of termination, which it almost certainly does, and (b) we don't know any of the underlying facts about the alleged police letter.

A court action might bring some facts to light, but it's unlikely to reinstate the service.

European Court of Human Rights is also not exclusive to European Union, other countries signed the convention as well and ratified at least parts of it. There appeals can reach ECHR and its rulings have to be enforced locally.