Integrating Rails and React may be a good idea if most of your business logic resides on the backend and sharing code across client and server is not particularly beneficial. Rails stack provides you with great ORMs (for both SQL and NoSQL databases) and gems to simplify repetitive things (authentication, authorization, permission systems, user management, auditing etc.) and has good tooling around strong cohesive conventions.
While I work on node full time now, I miss the strong focus on conventions in the Ruby community.
Solutions are react-rails (which integrate React in Rails asset pipeline) are great if either you are already using sprockets extensively or need to use React only in specific parts of your application.
If instead you are starting out with a new React+Redux/Flux application where most or all the frontend is managed through React, I would recommend you to use javascript based toolchains (Webpack or browserify) for managing your frontend assets and using Rails for the backend API only and not using the view layer or asset pipeline at all. Rails API makes this a lot easier. For server side rendering hypernova by Airbnb is a great solution.