I'm likely giving a talk on this exact subject in January (depending on scheduling). If you're curious about the various approaches I've tried, you can reach me at this username in all sorts of places.
I think you'd use Django REST framework wouldn't you?
I recently just started replacing some jQuery functionality with React in a large Django project, using Django-Rest, it's actually been less complicated than I expected.
Why can't you just serve up your react js assets like any other js asset when using django?