Let's combine two Nuxt 2 plugins : nuxt-i18n and @nuxtjs/auth

First we need to create a new @nuxtjs/auth plugin. This is fairly easy !

Let's assume that the user's language preference is indicated in the language property of the user object.

// plugins/auth/locale.js

export default ({ app, $auth }) => {
    $auth.onRedirect((to, from) => {
        app.i18n.setLocale($auth.user.language)
    })
}

Next, register the plugin in

// nuxt.config.js

auth: {
    plugins: [
        '~/plugins/auth/locale',
    ],
}