TL;DR: you can use an EUPL library in your proprietary application.

There are lots of information about this topic on the official website of the European Union.
It all says: virality does not exist legally in Europe, even for the GPLv3 or AGPLv3. And you are bound to the EU law for the code corresponding to EUPL. While the FSF wishes there is virality and tries to enforce it as much as they can with their own GNU licenses, the EU did not intend that in any way. The EUPL is closer to the MPL or EPL in intention than to the GPL.

https://joinup.ec.europa.eu/collection/eupl/news/eupl-and-proprietary-commer

https://joinup.ec.europa.eu/solution/eupl-freeopen-source-software-licence-european-union/about

https://joinup.ec.europa.eu/collection/eupl/news/why-eupl-not-viral-l

https://joinup.ec.europa.eu/collection/eupl/news/meaning-copyleft

https://joinup.ec.europa.eu/collection/eupl/news/why-viral-licensing-ghost