You can achieve that by creating an API with Django, you create a route that serves an HTML file with your React app script attached.
Then in your React app, you just make calls to your Django API, and TADAAA! You have your fully working React/Django app, then you can join the awesome club of React developers!
For the server side rendering, I don't know if libs exist for that, but as a backup solution, you could install node on your server, build a little utils script that accepts an input file and sends back the stringified rendering. Then in your Django back end you make a call to the utils script with the path to your react app js file, take the output and put it in your template.
TADAAAAAA! ( again ) Once your solution is fully implemented, you are ready to ROCK with your JS/PYTHON stack :)