Regardless of how you paid or where you live and focusing on the question "what does the law say", they offered you a service and you accepted (even paid), so you have a presumably valid contract (i.e. assuming you aren't confused about what they offered). They are required, therefore, to provide the contracted service, so they would appear to be in breach of that contract. The legal remedy is to sue them for damages, and assuming they are found liable, the court could order them to make good on the agreement, or to compensate you, which would certainly include the cost that you paid.
In this particular case, you may have a problem regarding what you bought. Owing to their problems with the US government and having been shut down, it is not clear to me that they are actually in breach – it looks to me like they are selling half-price reservations for future subscriptions, and have not promised to make the service immediately available. Their (findable) web pages do not seem to actually articulate anything resembling a sales agreement; they do say that (as of the January limited release) it is a limited release, which allowed existing customers to migrate their credentials. So one further analysis of the situation is that they were actually offering a future right to a service, and you believed that you were receiving an immediate service. There was a mistake, maybe meaning that there was no agreement (contract) in the first place. In which case, the company would have no contractual right to your money: the contract might be cancelled.
However, it is not sufficient to say "But I thought...", since otherwise no contracts would ever be valid. The question would be whether the seller knew or should have known that your belief was mistaken. You would need professional legal advice, to evaluate the case that the seller has any responsibility in this instance, but insofar as it seems reasonably clear that they are not actually offering current email service, then "caveat emptor" would work against you: you should have known that you weren't getting immediate service.
If you are in some other country, such a France, then there might be specific country-specific consumer protection laws.