At the moment there is a Fortnite event taking place, which brings the servers to their knees - so Fortnite is currently down. Also the Epic Games Launcher is not usable at the moment - you can't register.
Article at 20:03: Again and again certain services have to struggle with server problems, especially when there is a lot of server load. This is currently available at Fortnite due to a special event and therefore Fortnite itself is anyway also the Epic Games Launcher currently down. Today the first chapter of Fortnite ends and at 8 pm you want to finish it with a special event. Interested people can't play anymore - the registration servers are completely down.
Fortnite down: What to do?
At the moment you can't do more than wait and see. On the status page of Epic Games you won't find really helpful information - there the service is indicated as online and working. If you can't play, you can search for Fortnite streams on Twitch and watch them there. If you don't restart your game, you are stuck in the login window of the Epic Game Launcher. Then you won't get into the game at all today.
Fortnite down: All updates