To be effective in countering misinformation, it is paramount for fact-checkers to reach a wide audience. This study investigates the dynamics that lead to broader engagement with fact-checking content published on social networks. Specifically, it analyzes the dissemination activity on Twitter of a cross-national sample of European fact-checkers over a span of 4 months. We employ Network Analysis and Natural Language Processing techniques (sentiment analysis and keyword extraction), to address four questions: 1. Are there specific tweets that attract the majority of engagement?; 2. Do these tweets draw engagement from audiences beyond their usual reach?; 3. What is the prevailing sentiment expressed in these tweets—positive, neutral, or negative?; 4. What topics are covered in these highly engaging tweets? The results show that certain tweets receive significantly higher levels of engagement than the average and that this engagement extends beyond the typical audience. Furthermore, our findings suggest that while the topics of the most popular tweets are country-specific, audiences in most of the considered countries tend to interact more with tweets expressing negative sentiments.