How can I verify that a root certificate is authentic?
Authenticity can be kind of checked if you search for the fingerprint online and find the certificate where you would expect it. But this is not foolproof because this might be a fake site which is just looking good and has a trustable host name. In any case you don't know the party personally and authenticity does not mean that the party can be trusted.
At the end you have to trust the vendor of your OS or browser that it is doing the right thing, because effectively you have no way to really verify it. But this kind of trust is not uncommon, i.e. you trust your supermarket that the food is edible and not expired or even poisoned, you trust your gas station that the gasoline is not dangerous for your car ... - i.e. you already trust others in security issues. And you hope that if this trust is no longer justified you will somehow be notified.
Trust can go wrong as can be seen in the Superfish affair where one trusted the vendor (Lenovo) to ship a trustable computer. But this computer contained a software to injects ads and additionally the software installed its own root certificate to man-in-the-middle connections in order to inject ads into https traffic too. This certificate was definitely authentic, but most people would not consider it trustable.