Following Bourdieu and Passeron's concept of cultural capital, this article contributes to the study of its transmission within stable fractions of the working classes in France, who are less observed and yet central. On the basis of household monographs and national statistics, this inquiry confirms an overall large aspiration to academic achievement despite the cliché of a parental resignation regarding the academic and professional future of children. This aspiration is notable in academic choices and in homework monitoring. The educational investment of parents from this median section of contemporary working classes -- mothers especially -- can be explained by their modest, albeit not valueless, school capital. The secondary analysis of quantitative data illustrates a new distribution of diplomas among blue- and pink-collar workers. Repeated interviews show how school investments are deeply rooted in the academic and professional experience of those parents who frequently strive to catch up on a 'thwarted education' with continuing training.