Yes, there is such a system. The roads marked with a green label and letter E are marked in accordance with this system: E47 on the Denmark map is the European route 47, E1 on the Portugal map is the European route 1.
Quotation from WIkipedia:
In most countries, roads carry the European route designation beside
national road numbers. Other countries like Belgium, Norway and Sweden
have roads with exclusive European route signage (Examples: E 18 and E
6), while at the other end of the scale, British road signs do not
show the routes at all. Denmark uses exclusive European routes, but
uses also formal names for every motorway (or part of such), which the
motorways are referred to, for instance in news and weather forecasts.
This is the map these international roads:
All other names (not green) are national, and these roads may or may not be part of European routes. For example, 10 on the German map is A10 is Bundesautobahn 10, different parts of which belong to E26, E30, E51 and E55.
Here is a nice example of three diferent name systems for one road: Dutch A77 becomes A57 in Germany but still remains E31:
PS. Germany does not "simply use" numbers. It's Google Maps who simply uses numbers for German roads. Every German road has a letter in its name: A for Autobahn, B for Bundesstraße (federal highway), L for Landesstraße (regional/state road) and K for Kreisstraße (district/county road).