The long Swift gamma-ray burst GRB 120326A at redshift z = 1.798 exhibited a multi-band light curve with a striking feature: a latetime, long-lasting achromatic rebrightening, rarely seen in such events. Peaking in optical and X-ray bands ∼ 35 ks (∼ 12.5 ks in the GRB rest frame) after the 70-s GRB prompt burst, the feature brightens nearly two orders of magnitude above the underlying optical power-law decay. Modelling the multiwavelength light curves, we investigate possible causes of the rebrightening in the context of the standard fireball model. We exclude a range of scenarios for the origin of this feature: reverse-shock flash, late-time forward shock peak due to the passage of the maximal synchrotron frequency through the optical band, late central engine optical/X-ray flares, interaction between the expanding blast wave and a density enhancement in the circumburst medium and gravitational microlensing. Instead we conclude that the achromatic rebrightening may be caused by a refreshed forward shock or a geometrical effect. In addition, we identify an additional component after the end of the prompt emission, that shapes the observed X-ray and optical light curves differently, ruling out a single overall emission component to explain the observed early time emission.