The GPLv3 and the EUPL licences are not (yet) compatible. Compatibility can either mean that a licence allows integration of software components, to distributed under a different licence. Or it means that specific licences, under certain conditions, can simply be used as alternatives. The EUPL, for instance, lists five alternative free software licences. But neither the GPLv3 or the EUPL mentions the other.
The EUPL, the European Union's free software licence, does not mention the GPLv3, as it had not been completely finished when the EUPL was created. In turn, the Free Software Foundation, author of the GPLv3, does not mention the EUPL, explaining on it's website that the EUPL "is incompatible with GPLv3, because recipients are not given permission to use GPLv3's terms, and the EUPL's copyleft conflicts with GPLv3's."
However, both licences allow developers that are the original authors of the free software code to allow exceptions to the way their own code is redistributed. Sencha used this option to add the EUPL to its list of compatible software libraries, after being contacted by OSOR, aiming to assist the development of two Italian free software projects.
The two projects, 'NotreDAM' for managing digital multi-media assets, and 'CreaTiVù', for collaborating on TV programmes, use Sencha's Ext JL components. Developers had considered to published their work using the EUPL. Both applications are now published under the GPLv3.
The EUPL was written by the European Union and version 1 was published in June 2007. The GPLv3 was written by the Free Software Foundation and published in June 2007. They are both copyleft licences, offering users the right to distribute and modify the source code, as long as the derivative work remains free software as well.
Sencha's GPLv3 compatability list
Building compatibility between the EUPLv1.1 and the Gnu GPLv3 (blog)
Comparing the EUPLv1.1 and the GPLv3 (blog)
GNU statement on EUPL - GPLv3 copyleft incompatability