React - Module parse failed

You need add babel-loader, with react preset, do the following steps

1. npm i --save-dev babel-loader babel-preset-react babel-preset-es2015

2. add to webpack.config.js configs for babel-loader ( to loaders: [..] section)

   {  
      test: /\.jsx?$/,
      exclude: /(node_modules)/,
      loader: 'babel',
      query: {
         presets: ['react', 'es2015']
      }
   }
   

Update: babel-preset-es2015, babel-preset-react was deprecated in favor of using @babel/env and @babel/preset-react

1. npm i --save-dev babel-loader @babel/core @babel/preset-react @babel/preset-env
2. add to webpack.config.js configs for babel-loader

  rules: [
    {
      test: /\.jsx?$/,
      exclude: /(node_modules)/,
      use: {
        loader: 'babel-loader',
        options: {
          presets: ['@babel/preset-env', '@babel/preset-react']
        }
      }
    }
  ]