We report here the first results of a multi-wavelength campaign focussing on magnetospheric accretion processes within the close binary system V4046 Sgr, hosting two partly-convective classical T Tauri stars of masses ~0.9 Msun and age ~12 Myr. In this paper, we present time-resolved spectropolarimetric observations collected in 2009 September with ESPaDOnS at the Canada-France-Hawaii Telescope (CFHT) and covering a full span of 7d or ~2.5 orbital/rotational cycles of V4046 Sgr. Small circularly polarised Zeeman signatures are detected in the photospheric absorption lines but not in the accretion-powered emission lines of V4046 Sgr, thereby demonstrating that both system components host large-scale magnetic fields weaker and more complex than those of younger, fully-convective cTTSs of only a few Myr and similar masses. Applying our tomographic imaging tools to the collected data set, we reconstruct maps of the large-scale magnetic field, photospheric brightness and accretion-powered emission at the surfaces of both stars of V4046 Sgr. We find that these fields include significant toroidal components, and that their poloidal components are mostly non-axisymmetric with a dipolar component of 50-100G strongly tilted with respect to the rotation axis; given the similarity with fields of partly-convective main-sequence stars of similar masses and rotation periods, we conclude that these fields are most likely generated by dynamo processes. We also find that both stars in the system show cool spots close to the pole and extended regions of low-contrast, accretion-powered emission; it suggests that mass accretion is likely distributed rather than confined in well defined high-contrast accretion spots, in agreement with the derived magnetic field complexity.