The kick-off of vaccination campaigns in Europe, starting in late December 2020, has been followed by the online spread of controversies and conspiracies surrounding vaccine validity and efficacy. We study Twitter discussions in three major European languages (Italian, German, and French) during the vaccination campaign. Moving beyond content analysis to explore the structural aspects of online discussions, our investigation includes an analysis of polarization and the potential formation of echo chambers, revealing nuanced behavioral and topical differences in user interactions across the analyzed countries. Notably, we identify strong anti- and pro-vaccine factions exhibiting heterogeneous temporal polarization patterns in different countries. Through a detailed examination of news-sharing sources, we uncover the widespread use of other media platforms like Telegram and YouTube for disseminating low-credibility information, indicating a concerning trend of diminishing news credibility over time. Our findings on Twitter discussions during the COVID-19 vaccination campaign in major European languages expose nuanced behavioral distinctions, revealing the profound impact of polarization and the emergence of distinct anti-vaccine and pro-vaccine advocates over time.