Background Cancer-incidence and mortality-trend analyses require appropriate statistical modelling. In countries without a nationwide cancer registry, an additional issue is estimating national incidence from local-registry data. The objectives of this study were to (i) promote the use of multidimensional penalized splines (MPS) for trend analyses; (ii) estimate the national cancer-incidence trends, using MPS, from only local-registry data; and (iii) propose a validation process of these estimates. Methods We used an MPS model of age and year for trend analyses in France over 1990–2015 with a projection up to 2018. Validation was performed for 22 cancer sites and relied essentially on comparison with reference estimates that used the incidence/health-care ratio over the period 2011–2015. Alternative estimates that used the incidence/mortality ratio were also used to validate the trends. Results In the validation assessment, the relative differences of the incidence estimates (2011–2015) with the reference estimates were <5% except for testis cancer in men and < 7% except for larynx cancer in women. Trends could be correctly derived since 1990 despite incomplete histories in some registries. The proposed method was applied to estimate the incidence and mortality trends of female lung cancer and prostate cancer in France. Conclusions The validation process confirmed the validity of the national French estimates; it may be applied in other countries to help in choosing the most appropriate national estimation method according to country-specific contexts. MPS form a powerful statistical tool for trend analyses; they allow trends to vary smoothly with age and are suitable for modelling simple as well as complex trends thanks to penalization. Detailed trend analyses of lung and prostate cancers illustrated the suitability of MPS and the epidemiological interest of such analyses.