This paper provides empirical evidence on how aspirations are formed and affect individual behaviour, decisions and paths in the context of education. Using unique survey data merged with administrative data on French ninth graders, we show that low-SES students have lower aspirations than their equally-achieving high-SES classmates. Furthermore, academic track assignments to high school the next year are even more unequal due to dysfunctional dynamics: first, both low aspirations and low SES are associated with slower academic progression over the year. Second, aspirations and parent SES play a role in track assignment independently from one's academic performance. Our results suggest that in France an aspirational trap at school contributes to the poverty trap leading to the perpetuation of social inequalities.