example.jsx

// views/Documents.js
function Documents(props) {
    return (
        <ul>
            {props.documents.map((doc) => <li>{doc.id} - {doc.title}</li>)}
        </ul>
    )
}

Documents.propTypes = {
    documents: PropTypes.arrayOf(PropTypes.shape({
        id: PropTypes.string.isRequired,
        title: PropTypes.string.isRequired
    })).isRequired
};

// containers/Documents.js
// This is the file that is used by the router
class DocumentsContainer extends Component {
    static contextTypes = {
        hoodie: PropTypes.object.isRequired
    }

    componentWillMount() {
        const { hoodie } = this.context;
        const store = hoodie.store("documents");

        store.on("change", this.fetchDocuments.bind(this, store));

        this.fetchDocuments(store);
    }

    fetchDocuments(store) {
        store.findAll().then((documents) => {
            this.setState({
                documents: documents
            })
        })
    }

    render() {
        return <Documents documents={this.state.documents} />
    }
}

// index.js
var HoodieProvider = // https://gist.github.com/ThisIsMissEm/2a1babb16cbd8cd1123576e2c978b20a

var Hoodie = require('@hoodie/client')
var hoodie = new Hoodie({
  url: 'https://myhoodieapp.com',
  PouchDB: require('pouchdb')
})

ReactDOM.render(
    (
        <HoodieProvider hoodie={hoodie}>
            <DocumentsContainer />
        </HoodieProvider>
    ), document.getElementById("root")
);

not directly related to your challenges with Hoodie right now, but would recommend PouchDB: require('pouchdb-browser') over PouchDB: require('pouchdb')

You need to wait for the hoodie.ready promise to finish before you can use the hoodie.store or the hoodie.account APIs.