Typically I would not recommend you manage sessions on the front-end as it's easy to hack.
With JWT (JSON Web Tokens) you create a token on your backend and your front-end just requests the latest token. Inside that token will be info on whether that session is still active (you'd control what is returned).
Find a good JWT guide set it up, then from React you make a simple fetch command to get the JWT and then parse it and boot the user as necessary.
There was a similar question to yours asked earlier in the year, please see below:
What is the best way to manage a user's session in React?