Will my Laptop be able to run Fortnite well?

Yes it should

You left out the most important part: the graphics card. Most laptops have terrible integrated graphics cards. They're fine for videos, web browsing, general desktop use, etc, but terrible for gaming. If your laptop has a dedicated graphics card (something like a GTX 1050 Ti, or similar), then it should be ok for some gaming.

What kind of video card does it have? Know fortnite is not a very demanding game so it might run even on onboard graphics but you will have to lower the settings and if you don't mind playing at 30 fps then it should work. But even an xbox one would be smother then a laptop with intel hd graphics.

You should look up the specs required & compare with the laptop's & see.

Go to game-debate.com and enter the pc details and it will tell you.

You don't state whether you have a graphics card or if you're using the GPU within the CPU.

If you have a separate graphics card, then it'll be fine. If not, then you'll find out when you install it.
The worst that will happen is that you have to lower the graphics settings to low.

Without knowing what sort of GPU it has, we can only assume that it's the Intel integrated GPU. If it's that GPU then no, it won't run Fortnight very well.