You can run it through the Apache proxy, but it would have to be running in a virtual directory (e.g. http://mysite.something/myreactapp ).
This may seem sort of redundant but if you have other pages that are not part of your React app (e.g. PHP pages), you can serve everything via port 80 and make it apear that the whole thing is a cohesive website.
1.) Start your react app with npm run, or whatever command you are using to start the node server. Assuming it is running on http://127.0.0.1:8080
2.) Edit httpd-proxy.conf and add:
ProxyRequests On
ProxyVia On
<Proxy *>
Order deny,allow
Allow from all
</Proxy>
ProxyPass /myreactapp http://127.0.0.1:8080/
ProxyPassReverse /myreactapp http://127.0.0.1:8080/
3.) Restart Apache