Background: Schools were closed extensively in 2020–21 to counter SARS-CoV-2 spread, impacting students' education and wellbeing. With highly contagious variants expanding in Europe, safe options to maintain schools open are urgently needed. By estimating school-specific transmissibility, our study evaluates costs and benefits of different protocols for SARS-CoV-2 control at school. Methods: We developed an agent-based model of SARS-CoV-2 transmission in schools. We used empirical contact data in a primary and a secondary school and data from pilot screenings in 683 schools during the alpha variant (B.1.1.7) wave in March–June, 2021, in France. We fitted the model to observed school prevalence to estimate the school-specific effective reproductive number for the alpha (Ralpha) and delta (B.1.617.2; Rdelta) variants and performed a cost–benefit analysis examining different intervention protocols. Findings: We estimated Ralpha to be 1·40 (95% CI 1·35–1·45) in the primary school and 1·46 (1·41–1·51) in the secondary school during the spring wave, higher than the time-varying reproductive number estimated from community surveillance. Considering the delta variant and vaccination coverage in Europe as of mid-September, 2021, we estimated Rdelta to be 1·66 (1·60–1·71) in primary schools and 1·10 (1·06–1·14) in secondary schools. Under these conditions, weekly testing of 75% of unvaccinated students (PCR tests on saliva samples in primary schools and lateral flow tests in secondary schools), in addition to symptom-based testing, would reduce cases by 34% (95% CI 32–36) in primary schools and 36% (35–39) in secondary schools compared with symptom-based testing alone. Insufficient adherence was recorded in pilot screening (median ≤53%). Regular testing would also reduce student-days lost up to 80% compared with reactive class closures. Moderate vaccination coverage in students would still benefit from regular testing for additional control—ie, weekly testing 75% of unvaccinated students would reduce cases compared with symptom-based testing only, by 23% in primary schools when 50% of children are vaccinated. Interpretation The COVID-19 pandemic will probably continue to pose a risk to the safe and normal functioning of schools. Extending vaccination coverage in students, complemented by regular testing with good adherence, are essential steps to keep schools open when highly transmissible variants are circulating. Funding: EU Framework Programme for Research and Innovation Horizon 2020, Horizon Europe Framework Programme, Agence Nationale de la Recherche, ANRS–Maladies Infectieuses Émergentes