Bear in mind that the mapping is pretty large, several GB. You need to leave the Zumo connected up to the PC with Garmin Express running for some hours for the update to complete.
Can you expand on what you mean by "I have hardly any mapping"?
If the mapping you can see is very basic with just major cities/towns and only major roads represented as mostly straight lines then you're seeing the basemap rather than the detailed mapping. It's either not installed or not active. Go to Tools > Settings > Map > Map Info and see if you have City Nav Europe (CN Europe NT 2014.4 or 2015.1 probably) checked. There should be two in there, one followed by 3D, this is less important.
