Context. The G-type star GJ504A is known to host a 3–35 M_Jup companion whose temperature, mass, and projected separation all contribute to making it a test case for planet formation theories and atmospheric models of giant planets and light brown dwarfs. Aims. We aim at revisiting the system age, architecture, and companion physical and chemical properties using new complementary interferometric, radial-velocity, and high-contrast imaging data. Methods. We used the CHARA interferometer to measure GJ504A’s angular diameter and obtained an estimation of its radius in combinationwith the HIPPARCOS parallax. The radius was compared to evolutionary tracks to infer a new independent age range for the system. We collected dual imaging data with IRDIS on VLT/SPHERE to sample the near-infrared (1.02–2.25 μm) spectral energy distribution (SED) of the companion. The SED was compared to five independent grids of atmospheric models (petitCODE,Exo-REM, BT-SETTL, Morley et al., and ATMO) to infer the atmospheric parameters of GJ 504b and evaluate model-to-model systematic errors. In addition, we used a specific model grid exploring the effect of different C/O ratios. Contrast limits from 2011 to 2017 were combined with radial velocity data of the host star through the MESS2 tool to define upper limits on the mass of additional companions in the system from 0.01 to 100 au. We used an MCMC fitting tool to constrain the companion’sorbital parameters based on the measured astrometry, and dedicated formation models to investigate its origin. Results. We report a radius of 1.35 ± 0.04 R_⊙ for GJ504A. The radius yields isochronal ages of 21 ± 2 Myr or 4.0 ± 1.8 Gyr for the system and line-of-sight stellar rotation axis inclination of 162.4_−4.3^+3.8 degrees or 186.6_−3.8^+4.3 degrees. We re-detect the companion in the Y2, Y3, J3, H2, and K1 dual-band images. The complete 1–4 μm SED shape of GJ504b is best reproduced by T8-T9.5 objects with intermediate ages (≤ 1.5Gyr), and/or unusual dusty atmospheres and/or super-solar metallicities. All atmospheric models yield T_eff = 550 ± 50 K for GJ504b and point toward a low surface gravity (3.5–4.0 dex). The accuracy on the metallicity value is limited by model-to-model systematics; it is not degenerate with the C/O ratio. We derive log L∕L_⊙ = −6.15 ± 0.15 dex for the companion from the empirical analysis and spectral synthesis. The luminosity and T_eff yield masses of M = 1.3_−0.3^+0.6 M_Jup and M = 23₋₉⁺¹⁰ M_Jup for the young and old age ranges, respectively. The semi-major axis (sma) is above 27.8 au and the eccentricity is lower than 0.55. The posterior on GJ 504b’s orbital inclination suggests a misalignment with the rotation axis of GJ 504A. We exclude additional objects (90% prob.) more massive than 2.5 and 30 M_Jup with semi-major axes in the range 0.01–80 au for the young and old isochronal ages, respectively. Conclusions. The mass and semi-major axis of GJ 504b are marginally compatible with a formation by disk-instability if the system is 4 Gyr old. The companion is in the envelope of the population of planets synthesized with our core-accretion model. Additional deep imaging and spectroscopic data with SPHERE and JWST should help to confirm the possible spin-orbit misalignment and refine the estimates on the companion temperature, luminosity, and atmospheric composition.