Objective Although social inequalities in COVID-19 mortality by race, gender and socioeconomic status are well documented, less is known about social disparities in infection rates and their shift over time. We aim to study the evolution of social disparities in infection at the early stage of the epidemic in France with regard to the policies implemented. Design Random population-based prospective cohort. Setting From May to June 2020 in France. Participants Adults included in the Epidémiologie et Conditions de Vie cohort (n=77 588). Main outcome measures Self-reported anosmia and/ or ageusia in three categories: no symptom, during the first epidemic peak (in March 2020) or thereafter (during lockdown). Results In all, 2052 participants (1.53%) reported anosmia/ageusia. The social distribution of exposure factors (density of place of residence, overcrowded housing and working outside the home) was described. Multinomial regressions were used to identify changes in social variables (gender, class and race) associated with symptoms of anosmia/ageusia. Women were more likely to report symptoms during the peak and after. Racialised minorities accumulated more exposure risk factors than the mainstream population and were at higher risk of anosmia/ageusia during the peak and after. By contrast, senior executive professionals were the least exposed to the virus with the lower rate of working outside the home during lockdown. They were more affected than lower social classes at the peak of the epidemic, but this effect disappeared after the peak. Conclusion The shift in the social profile of the epidemic was related to a shift in exposure factors under the implementation of a stringent stay-at-home order. Our study shows the importance to consider in a dynamic way the gender, socioeconomic and race direct and indirect effects of the COVID-19 pandemic, notably to implement policies that do not widen health inequalities.