The study of gas-rich debris discs is fundamental to characterising the transition between protoplanetary discs and debris discs. Aims. We determine the physical parameters of the brightest gas-rich debris disc orbiting HD 141569A. We analyse images from the NOrthern Extended Millimeter Array (NOEMA) and the Atacama Large Millimeter/submillimeter Array (ALMA) in ^12^CO, ^13^CO J=2-1, and ^13^CO J=1-0 transitions. We incorporate ALMA archival data of the ^12^CO J=3-2 transition and present continuum maps at 0.87mm, 1.3mm, and 2.8mm. We use simple parametric laws with the Diskfit code and MCMC exploration to characterise the gas disc parameters and report a first attempt to characterise its chemical content with IRAM-30m. The continuum emission is equally shared between a compact (<50au) and a smooth, extended dust component (~350 au). Large millimetre grains seem to dominate the inner regions, while the dust spectral index is marginally larger in the outer region. The ^12^CO is optically thick, while ^13^CO is optically thin with tau_13CO_~0.15 (C^18^O is not detected). The ^13^CO surface density is constrained to be one order of magnitude smaller than around younger Herbig Ae stars, and we derive a gas mass M_12CO_=10^-1^M_{sun}_. We confirm the presence of a small CO cavity (R_CO_=17+/-3au), and find a possibly larger radius for the optically thin ^13^CO J=2-1 transition (35+/-5au). We show that the observed CO brightness asymmetry is coincident with the complex ring structures discovered with VLT/SPHERE in the inner 90au. The ^12^CO temperature T_0_(100au)~30K is lower than expected for a Herbig~A0 star, and could be indicative of subthermal excitation. With the largest amount of dust and gas among hybrid discs, HD141569A shows coincident characteristics of both protoplanetary discs (central regions), and debris discs at large distance. Together with its morphological characteristics and young age, it appears to be a good candidate to witness the transient phase of gas dissipation, with an apparently large gas-to-dust ratio (G/D>100) favouring a faster evolution of dust grains.