Patent applications are secret, not to mention that software patents can be very difficult to interpret and search for. RMS gave a fairly long talk about the various problems with software patents[1], and the difficulty in being able to find all software patents that may be related to a project is one of them.
Patent applications are public for a minimal time period, 18 months at the very most. But obviously patents are public. React has been open source for over 2 years now. It's highly-likely, almost certain, that any React-related Facebook patent would now be public.
The second part of my comment is probably more applicable (maybe I should've just excluded the point about private patent applications). Even if a React-related patent was public, it wouldn't be called "Patent on React Framework". It probably wouldn't even use the words JavaScript, HTML, or DOM. You would need to hire a patent lawyer for an extended period of time to have a reasonable amount of certainty that no such patent exists (and even then, it's just an educated guess).
Yes, but for what patent? People have looked; none have been found. :)