The efficacy of digital contact tracing against COVID-19 epidemic is debated: smartphone penetration is limited in many countries, non-uniform across age groups, with low coverage among elderly, the most vulnerable to SARS-CoV-2. We developed an agent-based model to precise the impact of digital contact tracing and household isolation on COVID-19 transmission. The model, calibrated on French population, integrates demographic, contact-survey and epidemiological information to describe the risk factors for exposure and transmission of COVID-19. We explored realistic levels of case detection, app adoption, population immunity and transmissibility. Assuming a reproductive ratio R=2.6 and 50% detection of clinical cases, a ~20% app adoption reduces peak incidence of ~36%. With R=1.7, >30% app adoption lowers the epidemic to manageable levels. Higher coverage among adults, playing a central role in COVID-19 transmission, yields an indirect benefit for elderly. These results may inform the inclusion of digital contact tracing within a COVID-19 response plan.