In the Algerian EMI context, students may need certain learning factors which can help them obtain a favourable use of English and content, hence, boosting their learning engagement. Therefore, it is significant to explore how student learning engagement is affected by learning factors in EMI courses. This cross-sectional study aimed to investigate the influence of psychological and social factors on engineering students’ engagement with both English language and content knowledge in their EMI course. To achieve this aim and answer the research question of how psychological and social factors affect engineering students’ engagement in EMI courses, a structural model of the effects of the suggested learning factors on student engagement was constructed. Quantitative data was collected from a total of 168 students who have been selected by using a convenience sampling method. The participants received an online self-report questionnaire to complete after their engagement in EMI courses. The obtained data was then analysed using a Structural Equation Modelling (SEM) approach. The findings show that motivation, attitudes, and anxiety have significantly affected students’ engagement with both English language and content knowledge. In addition, presence, interaction, and cooperation had significant effects on student engagement with English language, and they demonstrated a significant effect on student engagement with content knowledge. Finally, implications for stakeholders in Algeria and other non-Anglophone African, Asian, and European countries may expose new prospects for providing innovative techniques and platforms for EMI courses in higher education and familiarizing students with knowledge abilities before enrolling in EMI courses.