Your definition is very...unintuitive to me. Control inversion (the Hollywood Principle) isn't relevant -- many systems which use it aren't remotely frameworks.
Most people view libraries as tools which target narrowly scoped sub-problems of a given solution/application. In React's case, it's a view library -- the V in MVC, for instance. Frameworks are generally considered holistic set of tools which tightly integrate together to form a structured & opinionated approach to the larger solution, e.g the entire MVC approach.
React is widely considered a library. React doesn't tell you how to structure your project, manage its backend communication, handle application state, routing, etc. React is just...not a framework. For any standard notion of what engineers mean when using the term. If you use IoC to distinguish libs/frameworks, you're going to confuse the hell outta people. There are certainly technologies which straddle the line between these terms, but React is not one of them.