The long-term incorporation of immigrant-origin populations is a crucial question in liberal democracies. While much research has focused on the second generation, less is known about the grandchildren of immigrants. Investigating this “third generation” is key to assessing whether migration societies offer equal opportunity to their members regardless of their origins—that is, whether family background shapes life chances in a similar way among immigrant and native families. Here, we gauge the influence of ethnoracial origins on life chances in the long run by studying trajectories of intergenerational educational mobility among immigrant and native families over three generations. Our study is set in France, a major country of immigration in Europe, where a national narrative of immigrant integration and equality across ethnic origins has long prevailed. We show substantial catching up in educational attainment and higher social fluidity in immigrant families, for whom the grandparental educational starting point was very low. The grandchildren of Southern European immigrants converge with natives in their mobility patterns, suggesting equal opportunities. Despite a partial convergence, the grandchildren of North African immigrants experience a distinct mobility regime and enduring educational disadvantage. Altogether, our results suggest the existence of an ethnoracial hierarchy, whereby Southern European families experience educational destinies broadly comparable to those of natives, while ethnoracial origins durably shape the educational trajectories of North African families.