Firebase uses WebSockets, which currently is not supported by React Native. As of now, there is no good solution to integrate Firebase with React Native.
In lieu of requiring firebase as a module, you can indeed use the firebase API instead. If you were doing a simple get request, your fetch function would look like this:
var url = "https://YourDatabaseName.firebaseio.com/some/val.json";
fetch(url)
.then((response) => response.json())
.then((responseData) => {
console.log(responseData);
})
.done();
For more information, you can check out a blog post I wrote about the topic here:
http://anuj.io/using-firebase-api-with-react/