The European Patent Convention does not contain any disposition related with a Compulsory License Regime, which means that it is not possible to issue a Compulsory License under the EPC regime.
Therefore, each country shall regulate the Compulsory Licenses Regime on a national level. In that regard, the European Commission answered to a series of questions on the topic put by some of its members:

European Commission. Parliamentary questions: Answer given by Ms. Bienkowska on behalf of the Commission to questions P-00227/2015, P-00293/2015 and E-000205/2015. (2015)