gs_spreadsheet_example

contact_me.js

...
$.ajax({
  url: "https://script.google.com/macros/s/AKfycbz4aFabJ80gajXFBcXlFLpR6n9ad9GHs4UcT6ux9w7RAYcI_9w/exec",
  // this was 'url: "././mail/contact_me.php"'
  type: "POST",
  data: {
    name: name,
    phone: phone,
    email: email,
    message: message
  },
  ...
  success: function() {
    // Show success message on website
    ...
  },
  error: function() {
    // Show error message on website
    ...
  },
})
...