Exemple on how to get the user current postcode using Google map Geocoding API and HTML5 Geolocation (Navigator.geolocation).

<script
  src="https://maps.googleapis.com/maps/api/js?key=[Your Key]"
  async
  defer
></script>

(function() {
  document.addEventListener("DOMContentLoaded", event => {
    if (navigator.geolocation) {
      getCurrentLocation.location();
    }
  });

  const getCurrentLocation = {
    success: function(position) {
      const _this = this;
      const geocoder = new google.maps.Geocoder();
      const latlng = {
        lat: position.coords.latitude,
        lng: position.coords.longitude
      };
      let result = {
        error: false,
        value: ""
      };

      geocoder.geocode({ location: latlng }, (results, status) => {
        if (status === "OK") {
          if (results[0]) {
            const resultsData = results[0].address_components;

            for (let addressComponent of resultsData) {
              if (addressComponent.types.indexOf("postal_code") > -1) {
                result.value = addressComponent.long_name;
                console.log(result.value);
              }
            }
          } else {
            result.error = true;
            _this.error(result.error);
          }
        } else {
          result.error = true;
          _this.error(result.error);
        }
      });
    },
    error: function(error = true) {
      if (error.code > 0 || error === true) {
        console.log("Sorry we couldn't find your current location");
      }
    },
    location: function() {
      const _this = this;

      navigator.geolocation.getCurrentPosition(
        position => {
          _this.success(position);
        },
        positionError => {
          _this.error(positionError);
        }
      );
    }
  };
})();

Sources