How to pass data from child component to its parent in ReactJS?

This should work. While sending the prop back you are sending that as an object rather send that as a value or alternatively use it as an object in the parent component. Secondly you need to format your json object to contain name value pairs and use valueField and textField attribute of DropdownList

Short Answer

Parent:

<div className="col-sm-9">
     <SelectLanguage onSelectLanguage={this.handleLanguage} /> 
</div>

Child:

handleLangChange = () => {
    var lang = this.dropdown.value;
    this.props.onSelectLanguage(lang);            
}

Detailed:

EDIT:

Considering React.createClass is deprecated from v16.0 onwards, It is better to go ahead and create a React Component by extending React.Component. Passing data from child to parent component with this syntax will look like

Parent

class ParentComponent extends React.Component {

    state = { language: '' }

    handleLanguage = (langValue) => {
        this.setState({language: langValue});
    }

    render() {
         return (
                <div className="col-sm-9">
                    <SelectLanguage onSelectLanguage={this.handleLanguage} /> 
                </div>
        )
     }
}

Child

var json = require("json!../languages.json");
var jsonArray = json.languages;

export class SelectLanguage extends React.Component {
    state = {
            selectedCode: '',
            selectedLanguage: jsonArray[0],
        }

    handleLangChange = () => {
        var lang = this.dropdown.value;
        this.props.onSelectLanguage(lang);            
    }

    render() {
        return (
            <div>
                <DropdownList ref={(ref) => this.dropdown = ref}
                    data={jsonArray} 
                    valueField='lang' textField='lang'
                    caseSensitive={false} 
                    minLength={3}
                    filter='contains'
                    onChange={this.handleLangChange} />
            </div>            
        );
    }
}

Using createClass syntax which the OP used in his answer Parent

const ParentComponent = React.createClass({
    getInitialState() {
        return {
            language: '',
        };
    },

    handleLanguage: function(langValue) {
        this.setState({language: langValue});
    },

    render() {
         return (
                <div className="col-sm-9">
                    <SelectLanguage onSelectLanguage={this.handleLanguage} /> 
                </div>
        );
});

Child

var json = require("json!../languages.json");
var jsonArray = json.languages;

export const SelectLanguage = React.createClass({
    getInitialState: function() {
        return {
            selectedCode: '',
            selectedLanguage: jsonArray[0],
        };
    },

    handleLangChange: function () {
        var lang = this.refs.dropdown.value;
        this.props.onSelectLanguage(lang);            
    },

    render() {

        return (
            <div>
                <DropdownList ref='dropdown'
                    data={jsonArray} 
                    valueField='lang' textField='lang'
                    caseSensitive={false} 
                    minLength={3}
                    filter='contains'
                    onChange={this.handleLangChange} />
            </div>            
        );
    }
});

JSON:

{ 
"languages":[ 

    { 
    "code": "aaa", 
    "lang": "english" 
    }, 
    { 
    "code": "aab", 
    "lang": "Swedish" 
    }, 
  ] 
}

To pass data from child component to parent component

In Parent Component:

getData(val){
    // do not forget to bind getData in constructor
    console.log(val);
}
render(){
 return(<Child sendData={this.getData}/>);
}

In Child Component:

demoMethod(){
   this.props.sendData(value);
 }