This week's free game on the Epic Games Store is the massive AAA title Grand Theft Auto V (GTA5).
You are able to get this epitome of the sandbox game genre for free until May 21st (May 22nd in Japan).
This isn't a limited free title, as long as you add it to your account within the promotional period then you will have access to the game permanently for free.
There's no need to download or install the game onto your PC, in fact you can add it your account even if you don't have a PC by accessing the store from the browser on your smartphone. (You will still need an Epic Games Store account)Epic Games Store
I guess I shouldn't be surprised that I wasn't able to connect to the store when I tried to check it out. But don't worry, it's available for the next week so just come back later and try again.
If you already have the Epic Games launcher installed on your PC then I hear that you'll have better luck accessing the store page from there, but this crash does also seem to be affecting the launcher as well. I'd say your best bet is still to wait and try again later.