UserForm.vue

<template>
  <!-- user form -->
</template>

<script>
export default {
  methods: {
      saveUser: function() {
        let formData = new FormData(document.getElementById(this.formId));
        window.axios.post('/users', formData)
        .then(
            res => {
                //process response
            },
            err => {
                if(err.response.data.errors.email) {
                    //email error from Laravel
                }
            }
        )
        .catch(err => {
            //catch error
        })
      }
  }
}
</script>