Both "EpicGamesLauncher" and "Fortnite" has been added to the content filter and set as "Allowed".
I also added allowed exceptions for "launcher.store.epicgames.com" and "egs-platform-service.store.epicgames.com" from the "Prevented content access" list on my sons dashboard in Bitdefender Central. There are no blocked websites which are easily associated with the actual Fortnite installation.
It's possible to log on to the Epic Games Launcher, but when trying to start Fortnite - login to the actual game fails and we get another login prompt. This fails as well and we get another login prompt. And so on.
As soon as I uninstalled the Bitdefender Parental Control application from his Windows installation everything started to work as normal again.
I have now given up and will not reinstall Parental Control on his computer until it's been fixed.