The game's requirements were pretty clear in my opinion... DirectX 12, Nvidia GTX 780 / AMD Radeon R9 290 as the minimum GPU. The R9 290 is a card that has been released in late 2013, yours unfortunately is even older.

If you want to upgrade I strongly suggest to start fresh instead of replacing things into your current rig, as it stands it's not worth it as the CPU would be a major bottleneck for any new decent piece of hardware you'd buy nowadays.

I have something very similar to your system (same CPU but 16 GB of RAM and a R7 270X) that I use as secondary desktop. It can still can rock non-demanding games but would never, ever be able to handle DX12 stuff decently... it could probably run HZD but it would constantly have choppy framerates even at minimum settings. It's a good machine, but well past its prime.