Rising social inequalities have become an important policy concern. In time of crisis, enhancing education is seen as a strategy to fight poverty and to ensure social and territorial cohesion. As an illustration, in 2010 the European Commission launched Europe 2020, a plan which aimed, among other things, to reduce school dropout. Several studies have focused on the links between school dropout and parental background, but less attention has been paid to variation across countries and trends over time. In this study, we want to fill this gap by using the European Labour Force Surveys (EU-LFS) of 26 countries, for the years 2004–2019. We focus on children aged 15–19, a key age group for completion of the upper-secondary level, which is necessary to access tertiary education. Results show that, in all European regions, children living with medium and highly educated parents, especially the mother, are more likely to be enrolled in formal education relatively to children with low educated parents. This effect seems to be more prominent in Central and South-Eastern European countries, while it is smaller in other regions of Europe. Changes over time show that only in some European regions the effect of parents’ education on children’s enrolment becomes weaker.