[Vuejs]-How to use .vue files with Rails 5.1

You have to make use webpack and you need to configure specific loader for vue file and another supporting loader. By googling itself you can find articles to build vue app from scratch(https://www.google.co.in/search?q=vuejs+webpack+starting).

For directory structure you may follow the vue-cli (https://github.com/vuejs-templates/webpack)