Individual differences in early academic skills at school entry are known to predict later academic outcomes, as demonstrated primarily by studies conducted in the United States (US). However, the mechanisms underlying this association remain unclear. In a country where early childhood education is more homogeneous than in the US (i.e., France), this study examined the strength of that predictive relationship and explored whether it could be partly explained by two domain-general mechanisms that are fundamental to effective learning in a school context: executive functions and children's ability to navigate social relationships. We measured math and reading skills in a cohort of 95 French children in both kindergarten and 5th grade, while also assessing their self-regulation, working memory, planning, theory of mind, and social behaviors at one or both time points. Results confirmed within- and cross-domain associations between early and later academic skills that were comparable to those found in previous studies. Self-regulation, working memory, and theory of mind all mediated both within- and cross-domain relationships. However, these mediations were systematically partial, meaning that early measures of academic achievement remained particularly strong predictors of later academic success. These findings suggest that domain-general cognitive processes, such as executive functions and social cognition, may play a role in explaining the relation between early and later academic achievement. However, a significant part of that relation may still be explained by domain-specific skill-building mechanisms.