ESLint configuration for JSX

In order to lint JSX files configuration alone is not enough. Your configuration looks fine (although you probably don't need babel-eslint, unless you are using features that are lower than stage 4 proposal). By default ESLint will only process .js files. You have to tell it that you want to process .jsx files as well by using --ext flag on command line: eslint --ext .jsx .

I found an alternative to the original answer so that you don't have to specify the arguments when running eslint command.

Option 1

Use the command eslint . --ext .js --ext .jsx

Option 2

Specify overrides in your eslint config...

//.eslintrc
{
  ...
  "overrides": [
    {
      "files": ["*.jsx", "*.js"]
    }
  ],
  ...
}

I would recommend you to use also the plugin for eslint https://github.com/yannickcr/eslint-plugin-react

You could do this example config:

'use strict';

module.exports = {
  'extends': [ 'plugin:react/recommended' ],
  'parserOptions': {
    'ecmaFeatures': {
      'jsx': true
    }
  },
  'plugins': [ 'react' ],
  'rules': {

    // React
    'react/forbid-prop-types': 'error',
    'react/no-multi-comp': [ 'error', { 'ignoreStateless': true }],
    'react/no-set-state': 'error',
    'react/no-string-refs': 'error',
    'react/prefer-es6-class': 'error',
    'react/prefer-stateless-function': 'error',
    'react/require-extension': 'error',
    'react/require-render-return': 'error',
    'react/self-closing-comp': 'error',
    'react/sort-comp': 'error',
    'react/sort-prop-types': 'error',
    'react/wrap-multilines': 'error',

    // JSX
    'react/jsx-boolean-value': 'error',
    'react/jsx-closing-bracket-location': 'error',
    'react/jsx-curly-spacing': [ 'error', 'always' ],
    'react/jsx-equals-spacing': 'error',
    'react/jsx-first-prop-new-line': 'error',
    'react/jsx-handler-names': 'error',
    'react/jsx-indent-props': [ 'error', 2 ],
    'react/jsx-indent': [ 'error', 2 ],
    'react/jsx-key': 'error',
    'react/jsx-max-props-per-line': [ 'error', { 'maximum': 3 }],
    'react/jsx-no-bind': 'error',
    'react/jsx-no-literals': 'off',
    'react/jsx-no-target-blank': 'error',
    'react/jsx-pascal-case': 'error',
    'react/jsx-sort-props': 'error',
    'react/jsx-space-before-closing': 'error'
  }
};