The COVID-19 pandemic deeply affected how schools and families functioned through most of 2020. In particular, school closures meant parents took on a more central role in their children’s learning. This study analyzed social class variations in the quantity and quality of homeschooling during the lockdown. Through an online questionnaire, 360 parents reported (1) their digital equipment and use, (2) the perceptions of their ability to homeschool their children, (3) how they handled homeschooling and (4) the extent to which they supported other activities considered more or less “profitable” from an educational point of view (e.g., reading, watching television). A social position index was used as a proxy of social class. The results indicated that all parents were highly involved in setting up homeschooling and that the lower the parents’ social position, the more they spent time homeschooling their children. However, in line with the digital divide literature, the lower the parents’ social position, the lower the digital equipment and the less the parents felt capable of homeschooling. Finally, the higher the social position of the families, the more children spent time doing activities considered to be “educationally profitable,” and the less they spent time doing “unprofitable activities.” Thus, even if all parents were highly involved in homeschooling, higher social position parents were better equipped both materially and psychologically to face the challenge of homeschooling. The long-term impact of these processes on the perpetuation of social class inequalities are discussed.