Background: several countries have implemented mobile apps in an attempt to trace close contacts of patients with COVID-19 and, in turn, reduce the spread of SARS-CoV-2. However, the effectiveness of this approach depends on the adherence of a large segment of the population. Objective: the aims of this study were to evaluate the acceptability of a COVID-19 contact tracing mobile app among the French population and to investigate the barriers to its use. Methods: the Health Literacy Survey 2019 questioned 1003 people in France during the COVID-19 pandemic on the basis of quota sampling. The survey collected sociodemographic characteristics and health literacy data, as well as information on participants" communication with caregivers, trust in institutions, and COVID-19 knowledge and preventive behaviors. The acceptability of a mobile app for contact tracing was measured by a single question, the responses to which were grouped into three modalities: app-supporting, app-willing, and app-reluctant. Multinomial logistic regression analysis was performed to identify the factors associated with the acceptability of a mobile app during the COVID-19 pandemic. Results: only 19.2% (193/1003) of all participants were app-supporting, whereas half of them (504/1003, 50.3%) were reluctant. The factors associated with willingness or support toward the contact tracing app included lower financial deprivation (app-willing: adjusted odds ratio [aOR] 0.8, 95% CI 0.69-0.93; app-supporting: aOR 0.7, 95% CI 0.58-0.84) and higher perceived usefulness of using a mobile app to send completed health questionnaires to doctors (app-willing: aOR 2.3, 95% CI 1.70-3.26; app-supporting: aOR 3.1, 95% CI 2.04-4.82). Furthermore, the likelihood of supporting the mobile app increased with age over 60 years (aOR 1.9, 95% CI 1.13-3.22), trust in political representatives (aOR 2.7, 95% CI 1.72-4.23), feeling concerned about the pandemic situation (aOR 2.2, 95% CI 1.47-3.32), and knowledge about the transmission of COVID-19 (aOR 2.0, 95% CI 1.39-2.96). Conclusions: the most socioeconomically precarious people, who are at a higher risk of SARS-CoV-2 infection, are also the most reluctant to using a contact tracing mobile app. Therefore, optimal adherence can only be effective with a targeted discourse on public health benefits to adopt such an app, which should be combined with a reduction in inequalities by acting on structural determinants.