The way I'm integrating Backbone and React that is very simple and has been working well is something like this:

    MyComponent = React.createClass({
        componentDidMount: function(){
            this.props.collection.on('request', function(){
    	       this.setState({loading: true});
            }.bind(this));

            this.props.collection.on('sync', function(){
    	       this.setState({loading: false});
            }.bind(this));

            this.props.collection.fetch();
        },
    });

Now you just write handlers to modify the collection and sync. setState takes care of triggering a render when your collection changes. As a bonus, you might want to render something different while in "loading" state.

If you don't want the component to own the collection (if you want to share a collection between multiple components), just pass it as a prop from a parent component; otherwise you can instantiate a new collection on getDefaultProps.