Correct me if I'm wrong, but it looks like React reinvents some things that have been in jQuery for years, like cross-browser event handling and DOM utilities. Why not build on top of jQuery?
If you're interested in using jQuery with React, we have an example: https://github.com/facebook/react/tree/master/examples/jquer.... It doesn't use XHR but it should give you some idea of how the 2 can play nicely together.