webpackのビルドをしても,ローカルの開発環境でエラーが出てしまいブラウザに何も表示されません

質問の主旨
現在、Reactを勉強中で本を読み進めてチャットアプリを作成しています。ですが、webpackのコンパイルでよく理解できないエラーが出てしまいうまくいきません。
ブラウザは立ち上がるのですが、画面が白いまま、エラーが出ます。
初心者なので、webpack周りのエラーのことを調べてみても結局よくわからないままです。

開発環境は以下の通りです。

インストールしたライブラリ

• Node.js
• Express
• React
• Socket.io / WebSocket

ディレクトリ

-chat
 -public
  -bundle.js
  -index.html
 -src
  - index.js
 - chat-server.js
 - package.json
 - package-lock.json
 -webpack.config.js

原因が分からないエラー

ERROR in ./src/index.js
Module build failed (from ./node_modules/babel-loader/lib/index.js):
Error: Plugin/Preset files are not allowed to export objects, only functions. In C:\Users\haruk\Documents\study\study-mcoding\11-React\chat\node_modules\babel-preset-es2015\lib\index.js
    at createDescriptor (C:\Users\haruk\Documents\study\study-mcoding\11-React\chat\node_modules\@babel\core\lib\config\config-descriptors.js:178:11)
    at items.map (C:\Users\haruk\Documents\study\study-mcoding\11-React\chat\node_modules\@babel\core\lib\config\config-descriptors.js:109:50)
    at Array.map (<anonymous>)
    at createDescriptors (C:\Users\haruk\Documents\study\study-mcoding\11-React\chat\node_modules\@babel\core\lib\config\config-descriptors.js:109:29)
    at createPresetDescriptors (C:\Users\haruk\Documents\study\study-mcoding\11-React\chat\node_modules\@babel\core\lib\config\config-descriptors.js:101:10)
    at passPerPreset (C:\Users\haruk\Documents\study\study-mcoding\11-React\chat\node_modules\@babel\core\lib\config\config-descriptors.js:58:96)
    at cachedFunction (C:\Users\haruk\Documents\study\study-mcoding\11-React\chat\node_modules\@babel\core\lib\config\caching.js:33:19)
    at presets.presets (C:\Users\haruk\Documents\study\study-mcoding\11-React\chat\node_modules\@babel\core\lib\config\config-descriptors.js:29:84)
    at mergeChainOpts (C:\Users\haruk\Documents\study\study-mcoding\11-React\chat\node_modules\@babel\core\lib\config\config-chain.js:320:26)
    at C:\Users\haruk\Documents\study\study-mcoding\11-React\chat\node_modules\@babel\core\lib\config\config-chain.js:283:7
    at buildRootChain (C:\Users\haruk\Documents\study\study-mcoding\11-React\chat\node_modules\@babel\core\lib\config\config-chain.js:68:29)
    at loadPrivatePartialConfig (C:\Users\haruk\Documents\study\study-mcoding\11-React\chat\node_modules\@babel\core\lib\config\partial.js:85:55)
    at Object.loadPartialConfig (C:\Users\haruk\Documents\study\study-mcoding\11-React\chat\node_modules\@babel\core\lib\config\partial.js:110:18)
    at Object.<anonymous> (C:\Users\haruk\Documents\study\study-mcoding\11-React\chat\node_modules\babel-loader\lib\index.js:144:26)
    at Generator.next (<anonymous>)
    at asyncGeneratorStep (C:\Users\haruk\Documents\study\study-mcoding\11-React\chat\node_modules\babel-loader\lib\index.js:3:103)
    at _next (C:\Users\haruk\Documents\study\study-mcoding\11-React\chat\node_modules\babel-loader\lib\index.js:5:194)
    at C:\Users\haruk\Documents\study\study-mcoding\11-React\chat\node_modules\babel-loader\lib\index.js:5:364
    at new Promise (<anonymous>)
    at Object.<anonymous> (C:\Users\haruk\Documents\study\study-mcoding\11-React\chat\node_modules\babel-loader\lib\index.js:5:97)
    at Object._loader (C:\Users\haruk\Documents\study\study-mcoding\11-React\chat\node_modules\babel-loader\lib\index.js:224:18)
    at Object.loader (C:\Users\haruk\Documents\study\study-mcoding\11-React\chat\node_modules\babel-loader\lib\index.js:60:18)
    at Object.<anonymous> (C:\Users\haruk\Documents\study\study-mcoding\11-React\chat\node_modules\babel-loader\lib\index.js:55:12)
npm ERR! code ELIFECYCLE
npm ERR! errno 2
npm ERR! chat@1.0.0 build: `webpack`
npm ERR! Exit status 2
npm ERR!
npm ERR! Failed at the chat@1.0.0 build script.
npm ERR! This is probably not a problem with npm. There is likely additional logging output above.

npm ERR! A complete log of this run can be found in:
npm ERR!     C:\Users\haruk\AppData\Roaming\npm-cache\_logs\2019-07-22T10_04_30_153Z-debug.log

webpack.config.json

const path = require('path')

module.exports = {
    mode: 'development',
    entry: path.join(__dirname,'src/index.js'),
    output: {
        path: path.join(__dirname,'public'),
        filename: 'bundle.js'
    },
    devtool: 'inline-source-map',
    module: {
        rules: [
            {
                test: /.js$/,
                loader: 'babel-loader',
                exclude: /node_modules/,
                options: {
                    presets: ['es2015','react','env']
                }
            }
        ]
    }

}

package.json

{
  "name": "chat",
  "version": "1.0.0",
  "description": "",
  "main": "public/bundle.js",
  "scripts": {
    "test": "echo \"Error: no test specified\" && exit 1",
    "build": "webpack"
  },
  "keywords": [],
  "author": "",
  "license": "ISC",
  "dependencies": {
    "express": "^4.17.1",
    "react": "^16.8.6",
    "react-dom": "^16.8.6",
    "socket.io-client": "^2.2.0",
    "socketio": "^1.0.0"
  },
  "devDependencies": {
    "@babel/core": "^7.5.5",
    "@babel/preset-react": "^7.0.0",
    "babel-core": "^6.26.3",
    "babel-loader": "^8.0.6",
    "babel-preset-es2015": "^6.24.1",
    "babel-preset-react": "^6.24.1",
    "webpack": "^4.36.1",
    "webpack-cli": "^3.3.6"
  }
}

追記

index.html

<!DOCTYPE html>
<html lang="en">
<head>
    <meta charset="UTF-8">
    <meta name="viewport" content="width=device-width, initial-scale=1.0">
    <meta http-equiv="X-UA-Compatible" content="ie=edge">
    <title>Document</title>
</head>
<body>
    <div id="root"></div>
    <script src="./bundle.js"></script>
</body>
</html>

chat-server.js

//リアルタイムチャットのサーバ

const express = require('express')
const app = express()
const server = require('http').createServer(app)
const portNo = 3001
server.listen(portNo, () => {
    console.log('open server',`http://localhost:${portNo}`)
})

app.use('/public',express.static('./public'))
app.get('/',(req,res) => {
    res.redirect(302,'/public')
})

const socketio = require('socket.io')
const io = socketio.listen(server)

io.on('connection',(socket) => {
    console.log('connet user', socket.client.id)
    socket.on('chat-msg' ,(msg) => {
        console.log('message',msg)
        io.emit('chat-msg',msg)
    })
})

index.js

 import React from 'react'
 import ReactDOM from 'react-dom'
 import socketio from 'socket.io-client'

 const socket = socketio.connect('http://localhost:3001')

 class ChatForm extends React.Component{
     constructor(props){
        super(props)
        this.state = {
            name: '',
            message: ''
        }
     }
     nameChanged(e){
         this.setState({message: e.target.value})
     }
     messageChanged(e){
         this.setState({message: e.target.value})
     }

     send(){
         socket.emit('chat-msg',{
             name: this.state.name,
             message: this.state.message
         })
         this.setState({message: ''})
     }
     render(){
         return(
             <div>
                 <p>名前: <br /></p>
                 <input value={this.state.name} onChange={e => this.nameChanged(e)} /><br />
                 <p>メッセージ: <br /></p>
                 <input value={this.state.message} onChange={e => this.messageChanged(e)}/><br />
                 <button onClick={e => this.send()}>送信</button>
             </div>
         )
     }
 }

 class ChatApp extends React.Component{
     constructor(props){
         super(props)
         this.state = {
             logs: []
         }
     }

     componentDidMount(){
         socket.on('chat-msg', (obj) => {
             const logs2 = this.state.logs
             obj.key = 'key_' + (this.state.logs.length + 1)
             console.log(obj)
             logs2.unshift(obj)
             this.setState({logs: logs2})
         })
     }
     render(){
         const messages = this.state.logs.map(e => (
             <div key={e.key}>
                 <span>{e.name}</span>
                 <span>: {e.message}</span>
             </div>
         ))
         return (
             <div>
                 <h1>chat</h1>
                 <ChatForm />
                 <div>{messages}</div>
             </div>
         )
     }
 }

 ReactDOM.render(
     <ChatApp />,
     document.getElementById('root')
 )

以上です。ご回答宜しくお願い致します。