There are two ways of getting a European wide trademark. Applying it directly at European Intellectual Property Office (EUIPO) or making an application for international trademark registration that covers also the European Union. If accepted, the registration covers all EU member states.
There are however some important differences depending which route you take.
Many companies who offer software products and services make a fundamental mistake in identifying those goods and services in their trademark application. With this simple rule you can do better than many other companies.