Few studies have used exploratory factor analysis (EFA) and exploratory bifactor factor analysis (EBFA) to define a baseline factor structure model checking the construct-relevant psychometric multidimensionality of student engagement. This study was conducted on a sample of 3,374 students in France, Wallonia-Brussels Federation, and Luxembourg by using EFA and EBFA, and by comparing four confirmatory factor models of student engagement in the classroom. Results indicated the relevance of a bifactor model to disentangle general and specific factors of student engagement in the classroom in relation with student misconduct at school. The study suggests that if student engagement is principally a unidimensional construct, specific latent dimensions also exist (e.g., specific boredom behaviors) that have a substantive value and must be specified to increase quality of measurement and predictive validity.