There's no technical reason why you can't use a combination of jQuery and React.
Though for most greenfield applications it would be advisable to pick or the other, depending on the current needs and future goals of the project.
There are a couple ways to facilitate interactions between components in React. In simple cases you can push 'props' and event handler functions downward from a shared root component into the relevant child components. For more complex applications it can be simpler to facilitate access to shared state (Redux is a popular library that provides this functionality).