I'm afraid the CPU is also too slow. Especially for Fortnite which seems to use a lot of CPU for some reason.
It's time to replace everything.
If I really really had to put money into this PC, I would get an used "RX 570" for ~50€ and a "XEON E3-1275 V2" for 30€ from Aliexpress. But that only makes it barely usable for 60FPS singleplayer games.
A good place to start would be to use your computer's resource monitor to see where it is bottlenecking while you play. If you can connect a second monitor or tv to your computer you can have it on that screen while you play and see what is tanking.
The CPU is really just too old at this point.
With a better GPU it might still be kinda ok for singleplayer games... but for multiplayer it will lag too much.
You should use task manager to see what is maxing out first.
Looking at the system requirements for Fortnight you are above the minimum but not by much and flipping just the GPU likely won't help.
That CPU is over a decade old and pairing it with a modern GPU will not be good.
But sadly replacing a CPU that old will also require a new mobo and therefore new ram.
The RAM should probably be upgraded anyway. DDR3 with 1600 clock speed isnt anything to write home about. I'd recommend OP price everything out and see if a prebuilt doesnt make more sense since it seems like it'll be a total rebuild.
I agree you should check to see what is causing the problem while you're in game. You can check by loading up Fortnite/CSGO and joining a game then pressing Ctrl + Shift + Esc to go to task manager. Click on the performance tab and you'll see charts for your CPU, GPU, memory and disk. If anything is above 90% usage it's causing a bottleneck. Hardware info can also help here if you want more information.
My hunch is that if stuttering is happening in Fortnite but not Minecraft or CSGO, it's the GPUs 2GB vram. If so, depending on your location you can pick up a used GPU for ~$75-100 that should work. LTT has a video about buying used GPUs but he does recommend more recent cards. I'd recommend an AMD Rx 590/Nvidia 1660 at minimum if you upgrade. The video recommends Nvidia 20 series and Rx 5700xt for a budget of $150-$200 as of a month ago. You can take the GPU, case, and SSD with you if you upgrade. Another cheap upgrade is 16gb of ram (Minecraft performance) and SSDs or even hard drives are cheap if you wanted to add more storage for your game library.
Thank you everyone for the the input!
I did like a couple of people suggested and played Fortnite with the performance monitor open. I was running the game in the performance mode, so the graphics were all the way down. It seems like the biggest bottleneck was actually the CPU which was running at around 90%, the GPU was running around 45%.
Based on these results and the comments here it doesn't really seem worth it to use this old computer. Will need to do some research on used parts and see what I can find in my area. Thanks again for the help!