Kepler-419 is a planetary system discovered by the Kepler photometry which is known to harbour two massive giant planets: an inner 3 M_J transiting planet with a 69.8-day period, highly eccentric orbit, and an outer 7.5 M_J non-transiting planet predicted from the transit-timing variations (TTVs) of the inner planet b to have a 675-day period, moderately eccentric orbit. Here we present new radial velocity (RV) measurements secured over more than two years with the SOPHIE spectrograph, where both planets are clearly detected. The RV data is modelled together with the Kepler photometry using a photodynamical model. The inclusion of velocity information breaks the MR⁻³ degeneracy inherent in timing data alone, allowing us to measure the absolute stellar and planetary radii and masses. With uncertainties of 12 and 13% for the stellar and inner planet radii, and 35, 24, and 35% for the masses of the star, planet b, and planet c, respectively, these measurements are the most precise to date for a single host star system using this technique. The transiting planet mass is determined at better precision than the star mass. This shows that modelling the radial velocities and the light curve together in systems of dynamically interacting planets provides a way of characterising both the star and the planets without being limited by knowledge of the star. On the other hand, the period ratio and eccentricities place the Kepler-419 system in a sweet spot; had around twice as many transits been observed, the mass of the transiting planet could have been measured using its own TTVs. Finally, the origin of the Kepler-419 system is discussed. We show that the system is near a coplanar high-eccentricity secular fixed point, related to the alignment of the orbits, which has prevented the inner orbit from circularising. For most other relative apsidal orientations, planet b’s orbit would be circular with a semi-major axis of 0.03 au. This suggests a mechanism for forming hot Jupiters in multiplanetary systems without the need of high mutual inclinations.