how to create common helper class in React JS using ES6 which is used by another component?

Create a file called helpers.js

//helpers.js

export const AjaxHelper = (url) => {
    return (
      //ajax stuff here
    );
}

Then in your component:

import React from 'react';
import {render} from 'react-dom';
import {AjaxHelper} from "./path/to/helpers.js"

class App extends React.Component {

    constructor(props) {
        super(props);
        let myajaxresult = AjaxHelper(url);
    }

    render () {
        return(
        <p> Hello React!</p>
        );
    }
}

There is one more approach by wrapping it by a class rather than keeping all methods open and floating around utils.js

//utilsjs
default export class Utils {
    static utilMethod = (data) => {
        return (
          //methods stuff here
        );
    }
}

and then in your component

import React from 'react';
import {render} from 'react-dom';
import Utils from "./utils"

 class App extends React.Component {

    constructor(props) {
        super(props);
        let myData = {}; // any arguments of your
        Utils.utilMethod(myData);

    }

    render () {
        return(
        <p> Hello React!</p>
        );
    }
}

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

The way that you've exported the class requires a new instance for each module you import it into. You can, instead, use a single instance as you've mentioned by exporting an instantiated AjaxHelperClass object rather than the class definition -- something like

export default new AjaxHelperClass();

This effectively gives you a global object. When importing the object, you can call its member functions i.e AjaxHelperClass.ResturantAPI();. Another option is to use static methods instead if all you want to use the class for is a namespace -- https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Classes/static