Whilst onegeology.org is great, and certainly there are a lot of European Geology WMS and some WFS services available. In this situation I think that currently (a) you might be better off going to the EGDI portal. European Geological Data Infrastructure (EGDI) is a collective project of the European Geological Surveys, and EGDI is intended to showcase all geological data sets available as OGC services that have been created by these survey organizations, which includes services that they have made available on OneGeology
As part of the creation of the EGDI portal the survey organizations revisited their harmonized geology services (some of the old services are available on the the soon to be retired OneGeology-Europe portal), updating the attribution to use the latest INSPIRE vocabularies, and are working to create both GeoSciML WFS and GeoSciML-Lite (portrayal) WMS, the latter of which will offer default styles based on the colours recommended by the INSPIRE geology data specification
For EGDI the geological survey organizations have also created a collective harmonized geology simple feature WFS of some of the attribution from their fuller (complex feature) WFS.
The service endpoint for simple feature WFS is:
So the WFS GetCapabilities is:
You get both age and lithology data sets for surface geology at a variety of scales. As it's a WFS you get the data to download as GML (shapefile is not available in this service), but you can use GIS software such as QGIS to convert the GML to a shapefile. As it's a WFS you don't get any styling. If you want to see styling for this data you can use the corresponding WMS, or if using QGIS you can apply the appropriate SLD as below:
(a): Eventually I expect that all harmonized geology services (WMS and WFS) will be available through the OneGeology Portal.
I work for a European geological survey organization, and have been involved in OneGeology, OneGeology-Europe, and the EGDI projects.