You can share some components, especially more abstract ones. For example, react-redux creates higher-order components that work with both React DOM and React Native. There's also a project called react-native-web that implements React Native's View components using React DOM's primitive components (
https://github.com/necolas/react-native-web).
Components aside, you can share your models and data stores, utilities like Immutable.js and lodash, and other environment-agnostic JavaScript. In addition to code, you can share a lot of knowledge like how to write components, structure an app, use npm, and even just write JavaScript.