We reconstructed the star formation histories of seven massive (M⋆ ≳ 1010 M⊙) early-type galaxies (ETGs) in the Virgo cluster by analysing their spatially resolved stellar population (SP) properties including their ultraviolet (UV) and Hα emission. As part of the Virgo Environmental Survey Tracing Ionised Gas Emission (VESTIGE), we used Hα images to select ETGs that show no signs of ongoing star formation. We combined VESTIGE with images from Astrosat/UVIT, GALEX, and CFHT/MegaCam from the Next Generation Virgo Cluster Survey (NGVS) to analyse radial spectral energy distributions (SEDs) from the far-UV (FUV) to the near-infrared. The UV emission in these galaxies is likely due to old, low-mass stars in post main sequence (MS) phases, the so-called UV upturn. We fitted the radial SEDs with novel SP models that include an old, hot stellar component of post-MS stars with various temperatures and energetics (fuels). This way, we explored the main stellar parameters responsible for UV upturn stars regardless of their evolutionary path. We make these models publicly available through the SED fitting code CIGALE. Standard models are not able to reproduce the galaxies' central FUV emission (SMA/Reff ≲ 1), while the new models well characterise it through post-MS stars with temperatures T ≳ 25 000 K. All galaxies are old (mass-weighted ages ≳10 Gyr) and the most massive ones, M49 and M87, are supersolar (Z ≃ 2 Z⊙) within their inner regions (SMA/Reff ≲ 0.2). Overall, we find flat age gradients (∇Log(Age) ∼ ‑0.04 ‑ 0 dex) and shallow metallicity gradients (∇Log(Z) < ‑0.2 dex), except for M87 (∇Log(ZM87) ≃ ‑0.45 dex). Our results show that these ETGs formed with timescales τ ≲ 1500 Myr, having assembled between ∼40 ‑ 90% of their stellar mass at z ∼ 5. This is consistent with recent JWST observations of quiescent massive galaxies at high-z, which are likely the ancestors of the largest ETGs in the nearby Universe. The derived flat and shallow stellar gradients indicate that major mergers might have contributed to the formation and evolution of these galaxies.