Smoking is a major preventable cause of cancers and is increasingly concentrated among the most deprived individuals leading to increasing socioeconomic inequalities in the incidence of cancers linked to smoking. We aimed to estimate the tobacco‐attributable cancer burden according to socioeconomic position in France. The analysis was restricted to cancer sites for which tobacco smoking was recognized as a risk factor. Cancer cases by sex, age group and European Deprivation Index (EDI) among people aged 30–74 between 2006 and 2009 were obtained from cancer registries covering ∼20% of the French population. The tobacco‐attributable burden of cancer according to EDI was estimated applying the population attributable fraction (PAF) computed with the Peto‐Lopez method. The PAF increased from 56% in the least deprived EDI quintile to 70% in the most deprived EDI quintile among men and from 26% to 38% among women. In total, 28% of the excess cancer cases in the four most deprived EDI quintiles in men and 43% in women could be prevented if smoking in these 4 EDI quintiles was similar to that of the least deprived EDI quintile. A substantial smoking‐attributable burden of cancer by socioeconomic position was observed in France. The results highlight the need for policies reducing tobacco consumption. More comprehensive interventions integrating the various dimensions of health determinants and proportionate according to socioeconomic position may essentially contribute to the reduction of socioeconomic inequalities in cancer.