Background The COVID-19 crisis and consequent confinement restrictions have caused significant psychosocial stress and reports of sleep complaints, which require early management, have increased during recent months. To help individuals concerned about their sleep, we developed a smartphone-based app called KANOPEE that allows users to interact with a virtual agent dedicated to autonomous screening and delivering digital behavioral interventions. Objective Our objective was to assess the feasibility of this app, in terms of inclusion rate, follow-up rate, perceived trust and acceptance of the virtual agent, and effects of the intervention program, in the context of COVID-19 confinement in France. Methods The virtual agent is an artificial intelligence program using decision tree architecture and interacting through natural body motion and natural voice. A total of 2069 users aged 18 years and above downloaded the free app during the study period (April 22 to May 5, 2020). These users first completed a screening interview based on the Insomnia Severity Index (ISI) conducted by the virtual agent. If the users were positive for insomnia complaints (ISI score >14), they were eligible to join the 2-stage intervention program: (1) complete an electronic sleep diary for 1 week and (2) follow personalized sleep recommendations for 10 days. We collected and analyzed the following measures: sociodemographic information, ISI scores and sleep/wake schedules, and acceptance and trust of the agent. Results Approximately 76% (1574/2069) of the app users completed the screening interview with the virtual agent. The virtual agent was well accepted by 27.4% (431/1574) of the users who answered the acceptance and trust questionnaires on its usability, satisfaction, benevolence, and credibility. Of the 773 screened users who reported sleep complaints (ISI score >14), 166 (21.5%) followed Step 1 of the intervention, and only 47 of those (28.3%) followed Step 2. Users who completed Step 1 found that their insomnia complaints (baseline mean ISI score 18.56, mean ISI score after Step 1 15.99; P<.001) and nocturnal sleep quality improved significantly after 1 week. Users who completed Step 2 also showed an improvement compared to the initial measures (baseline mean ISI score 18.87, mean ISI score after Step 2 14.68; P<.001). Users that were most severely affected (ISI score >21) did not respond to either intervention. Conclusions These preliminary results suggest that the KANOPEE app is a promising solution to screen populations for sleep complaints and that it provides acceptable and practical behavioral advice for individuals reporting moderately severe insomnia.