Context. Wide-field, multi-filter photometric surveys enable the reconstruction of the Milky Way's star formation history (SFH) on Galactic scales and provide complementary insights into disc assembly. The 12-filter system of the Javalambre Photometric Local Universe Survey (J-PLUS) is particularly suitable, as its colours trace stellar chemical abundances and help mitigate the age-metallicity degeneracy in colour-magnitude diagram fitting. Aims. We aim to recover the SFH of the Milky Way disc and separate its chemically distinct components by combining J-PLUS DR3 photometry with Gaia astrometry. We also intend to test the potential of isochrone fitting to estimate ages and metallicities for individual stars as proxies for disc evolutionary trends. Methods. We fitted magnitudes and parallaxes of 1.38 × 106 stars using a Bayesian multiple-isochrone technique. The bright region of the colour-absolute-magnitude diagram (Mr ≤ 4.2 mag) constrains stellar ages, while the faint region provides an empirical metallicity prior that mitigates the age-metallicity degeneracy. Both PARSEC and BaSTI isochrones, in solar-scaled and α-enhanced versions, were adopted. Results. The recovered SFH shows two sequences: an α-enhanced population forming rapidly between 12.5 and 8 Gyr ago, enriching from [M/H]~ −0.6 to 0.1 dex; and a solar-scaled sequence emerging ∼8 Gyr ago, dominating after ∼7 Gyr with slower enrichment and reaching solar metallicity by 3 Gyr. Metal-rich ([M/H] > 0) stars are confined to |zGC| ≲ 1 kpc, whereas metal-poor ([M/H] < -0.5) stars reach |zGC| ~ 2 kpc. Conclusions. Simultaneous fitting of solar-scaled and α-enhanced isochrones reveals distinct formation epochs for the thin and thick discs. J-PLUS multi-filter photometry, combined with Gaia parallaxes, effectively mitigates age-metallicity degeneracies and enables detailed mapping of the Milky Way's temporal and chemical evolution.