Hello Robin,
I guess you could join the zip code tables in order to form a single zip code data table that will be added as a single layer on your map chart.
To do this (if you are using the geocoding tables built-in Spotfire), simply browse to the Spotfire library under the GeoAnalytics folder where you will find the zip tables for these 3 countries. Start by importing one table (lets say USA Zip Codes). Once added to your analysis, add a next one (lets say France Postal Code) and you will see Spotfire suggesting to add it as rows to the first zip code table, as a join. Then do the same with the other zip code tables. This should do the trick. You will end up with a single zip code table.
Arnaud Varin's post in Zipcode Data for worldwide in Map chart was marked as the answer