You are most probably going to want to want to have separate package files as those two separate folders will have different tooling needs. That's not a must though. E.g. you may have a SSR React app that needs to be served. But... the way you explained it "client = React", "server = express" it sounds like you are building two separate integrated applications.

A more elaborated answer could include a way of working with workspaces where you may indeed want to have a root package.json