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Increased emergency medical services (EMS) response times and areas of low socioeconomic status are both associated with poorer outcomes for several time-sensitive medical conditions attended to by medical personnel before a patient is hospitalized. We evaluated the association between EMS response times, area deprivation level, and on-scene access constraints encountered by EMS in a large urban area in France. We conducted a multicenter prospective cohort study of EMS dispatches occurring in the forty-seven cities in a region southeast of Paris. We fit multilevel mixed-effects linear regression models for multivariate assessment of the predictors of EMS response times and then used multivariate logistic regression on outcomes among a subgroup of patients presenting with out-of-hospital cardiac arrest. We found evidence that access constraints were more frequently encountered by EMS in the most deprived areas compared to less deprived ones, and were associated with increased EMS response times until patient contact and with poorer outcomes from cardiac arrest. Strategies to anticipate and overcome access constraints should be implemented to improve outcomes for emergent conditions attended to by prehospital medical teams.