Action.js

import React from 'react';

export default class Action extends React.Component {
  constructor(props) {
    super(props);

    this.handleAction = this.handleAction.bind(this);
  }

  handleAction (e)  {
    e.preventDefault();
    // const movie = e.target.elements.movie.value;
    const query = e.target.query.value;
  }

  render() {
    return (
      <div>
        <form onSubmit={this.handleAction}>
          <input type='text' name='query'/>
        </form>    
      </div>
    );
  }
}

app.js

import React from 'react';
import ReactDOM from 'react-dom';

import MovieApp from './components/MovieApp';

ReactDOM.render(<MovieApp />, document.getElementById('app'));

MovieApp.js

import React from 'react';
import NewMovies from './NewMovies';
import Action from './Action';

export default class MovieApp extends React.Component {
  constructor(props) {
    super(props);

    this.state = {
      movie: "",
      movieSelected: false 
    }

    this.handleAction = this.handleAction.bind(this);
  }

  handleAction(query) {
    if (query) {
      this.setState(() => { movie: query });
    }
  }
  componentDidUpdate() {
    console.log('update!');
  }

  render() {
    return (
      <div>
        <Action
          handleAction={this.handleAction} 
        />
      </div>
    );
  }
}