Estimation of the impact of vaccination and non-pharmaceutical interventions (NPIs) on COVID-19 incidence is complicated by several factors, including the successive emergence of SARS-CoV-2 variants of concern and changing population immunity resulting from vaccination and previous infection. We developed an age-structured multi-strain COVID-19 transmission model framework that could estimate the impact of vaccination and NPIs while accounting for these factors. We applied this framework to French Polynesia, which unlike many countries experienced multiple large COVID-19 waves from multiple variants over the course of the pandemic, interspersed with periods of elimination. We estimated that the vaccination programme averted 54.3% (95% CI 54.0-54.6%) of the 6840 hospitalisations and 60.2% (95% CI 59.9-60.5%) of the 1280 hospital deaths that would have occurred in a baseline scenario without any vaccination up to May 2022. Vaccination also averted an estimated 28.4% (95% CI 28.2-28.7%) of 193,000 symptomatic cases in the baseline scenario. We estimated the booster campaign contributed 3.4%, 2.9% and 3.3% to overall reductions in cases, hospitalisations and hospital deaths respectively. Our results suggested that removing, or altering the timings of, the lockdowns during the first two waves had non-linear effects on overall incidence owing to the resulting effect on accumulation of population immunity. Our estimates of vaccination and booster impact differ from those for other countries due to differences in age structure, previous exposure levels and timing of variant introduction relative to vaccination, emphasising the importance of detailed analysis that accounts for these factors.