However, when I run npm run build, the process appears to execute correctly (creates build folder, which contains the bundled js file and the html.index file), but when I open index.html in my browser it renders nothing. What am I missing?
When you run npm run build, it prints the relevant instructions:
You can’t just open index.html because it is supposed to be served with a static file server.
This is because most React apps use client-side routing, and you can’t do that with file:// URLs.
In production, you can use Nginx, Apache, Node (e.g. Express), or any other server to serve static assets. Just make sure that if you use client-side routing, you serve index.html for any unknown request, like /*, and not just for /.
In development, you can use pushstate-server for this. It works with client-side routing well. This is exactly what the printed instructions suggest you to do.
I also tried uploading it to a remote server and when I went to the URL the browser came back with Forbidden: You don’t have permission to access / on this server.
You need to upload the contents of the build folder, not the build folder itself. Otherwise the server can’t find your index.html because it is inside build/index.html, and so it fails. If your server doesn’t detect a top-level index.html, please refer to your server’s documentation on configuring files served by default.