npm start won’t work on Netlify. See [Support Guide] Can I run a web server, HTTP listener, and/or database at Netlify? for why not.
You need to set the base directory to client.
Set the build command to npm run build
Set the publish directory to build (it will show client/build when the base directory is set to client)
See the React framework integration documentation and the Build from a subdirectory documentation for why you need to do this.