React implements the component lifecycle, calling into the component to do it, stores all the component state, and reconciles DOM changes on behalf of the component. It's the very definition of a framework - it's calls the component, the component doesn't call it.

It has been said it is a library, but imo it is not for the reason how it forces you to write code according to their rules. For instance functional components. Most of the code you write is to fit React, so for this reason I would say it is a framework.