vuejs2 multi-page not loading router-view

Question

I want to create a POC for multi-page app. I start with a basic app by doing vue create poc

then i add a second main.js named test.js with the same lines than the main.js

// main.js
import Vue from 'vue'
import App from './App.vue'
import './registerServiceWorker'
import router from './router'
import store from './store'

Vue.config.productionTip = false

new Vue({
  router,
  store,
  render: h => h(App)
}).$mount('#app')

// test.js
import Vue from 'vue'
import App from './App.vue'
import './registerServiceWorker'
import router from './router'
import store from './store'

Vue.config.productionTip = false

new Vue({
  router,
  store,
  render: h => h(App)
}).$mount('#app')

// vue.config.js
module.exports = {
  // https://cli.vuejs.org/config/#pages
  pages: {
    main: {
      // entry for the page
      entry: 'src/main.js',
      // the source template
      template: 'public/index.html',
      // output as dist/index.html
      //filename: 'index.html',
      // when using title option,
      // template title tag needs to be <title><%= htmlWebpackPlugin.options.title %></title>
      title: 'Multi-page Main',
      // chunks to include on this page, by default includes
      // extracted common chunks and vendor chunks.
      //chunks: ['chunk-vendors', 'chunk-common', 'index']
    },
    pasquier: {
      // entry for the page
      entry: 'src/test.js',
      // the source template
      template: 'public/index.html',
      // output as dist/index.html
      //filename: 'index.html',
      // when using title option,
      // template title tag needs to be <title><%= htmlWebpackPlugin.options.title %></title>
      title: 'Multi-page test',
      // chunks to include on this page, by default includes
      // extracted common chunks and vendor chunks.
      //chunks: ['chunk-vendors', 'chunk-common', 'index']
    },
    // when using the entry-only string format,
    // template is inferred to be `public/subpage.html`
    // and falls back to `public/index.html` if not found.
    // Output filename is inferred to be `subpage.html`.
    //subpage: 'src/subpage/main.js'
  }
}

The issue is that when I open my website with the url : localhost:8080/main I have :

I have the same exact page with localhost:8080/main

But when I load the app without the multi-page I have:

Which mean that the router-view is not loaded, but the router-link is. I didn't change any other code.

// App.vue
<template>
  <div id="app">
    <div id="nav">
      <router-link to="/">Home</router-link> |
      <router-link to="/about">About</router-link>
    </div>
    <router-view/>
  </div>
</template>

// router/index.js
import Vue from 'vue'
import VueRouter from 'vue-router'
import Home from '../views/Home.vue'

Vue.use(VueRouter)

const routes = [
  {
    path: '/',
    name: 'Home',
    component: Home
  },
  {
    path: '/about',
    name: 'About',
    // route level code-splitting
    // this generates a separate chunk (about.[hash].js) for this route
    // which is lazy-loaded when the route is visited.
    component: () => import(/* webpackChunkName: "about" */ '../views/About.vue')
  }
]

const router = new VueRouter({
  mode: 'history',
  base: process.env.BASE_URL,
  routes
})

export default router

How can i charge the root page / when using the multi-page ?