Context. Since the launch of the Fermi gamma-ray telescope, several hundred radio-loud gamma-ray pulsars have been detected, many belonging to millisecond pulsars but some belonging to the young pulsar population with spin periods longer than 30 ms.Aims. Observing simultaneously pulsed radio and gamma-ray emission from these stars helps to constrain the geometry and radiation mechanisms within their magnetosphere and to localize the multiple photon production sites. In this paper we fit the time-aligned gamma-ray light curves of young radio-loud gamma-ray pulsars. We assume a dipole force-free magnetosphere where radio photons emanate from high altitudes above the polar caps and gamma rays originate from outside the light cylinder, within the striped wind current sheet.Methods. We computed a full atlas of radio and gamma-ray pulse profiles depending on the magnetic axis obliquity and line-of-sight inclination with respect to the neutron star rotation axis. By applying a χ2 fitting technique, we were able to pin down accurately the magnetosphere geometry. Further constraints were obtained from radio polarization measurement following the rotating vector model, including aberration and retardation effects.Results. We find a good agreement between our model and the time-aligned single- or double-peaked gamma-ray pulsar observations. We deduce the magnetic inclination angle and the observer line of sight with respect to the rotation axis within a small error bar. The distinction between radio-loud or radio-quiet gamma-ray pulsars or only radio pulsars can entirely be related to the geometry of the associated emitting regions.Conclusions. The high-altitude polar cap model combined with the striped wind represents a minimalistic approach able to reproduce a wealth of gamma-ray pulse profiles for young radio pulsars. Based on self-consistent force-free simulations, it gives a full geometrical picture of the emission properties without resorting to detailed knowledge of the individual particle dynamics and energetics.