What we did to build our application in React. We created our whole application in React in Visual Studio Code with Redux and React-Router. Webpack is used to build all the files. Once whole application is completed, we build the js (transpiled and minified) and added a script tag pointing to that url of the bundle js into our web application page (specifically .aspx page).
Now issues you might face with react-router, if you have hosted it inside a directory of your existing project. For e.g. inside root - you have folder named myapp. If that is the case - you need to make changes to your Routes in your react app to have a base name.
I tried React.NET but after doing it this way - I really liked this approach as you can separately build the whole application with all the awesome tools you have in client side ecosystem - for instance - hot reloading
Hope it helps.
JavaScriptCode in server-sided.netApplications.