SpotLight doesn't seem to reflect off of my floor?

You’ve misunderstood. In your code sample, you are still using the MeshBasicMaterial

I am not even sure if you are asking the right question. You need to show a screen grab or a sample of what you are trying to achieve.

In the meantime, maybe this below is remotely similar to the answer you are trying to recieve, but I am still not convinced.

See the floor in this example. It is using a MeshPhongMaterial and not a MeshBasicMaterial
Spot Light Shadow - Three.js Tutorials (sbcode.net)
Use the Y slider.