We present a study of the cold gas contents of the Atlas3D early-type galaxies, in the context of their optical colours, near-UV colours, and Hbeta absorption line strengths. Early-type (elliptical and lenticular) galaxies are not as gas-poor as previously thought, and at least 40% of local early-type galaxies are now known to contain molecular and/or atomic gas. This cold gas offers the opportunity to study recent galaxy evolution through the processes of cold gas acquisition, consumption (star formation), and removal. Molecular and atomic gas detection rates range from 10% to 34% in red sequence early-type galaxies, depending on how the red sequence is defined, and from 50% to 70% in blue early-type galaxies. Notably, massive red sequence early-type galaxies (stellar masses > 5e10 Msun, derived from dynamical models) are found to have HI masses up to M(HI)/Mstar ~ 0.06 and H_2 masses up to M(H$_2$)/Mstar ~ 0.01. Some 20% of all massive early-type galaxies may have retained atomic and/or molecular gas through their transition to the red sequence. However, kinematic and metallicity signatures of external gas accretion (either from satellite galaxies or the intergalactic medium) are also common, particularly at stellar masses <= 5e10 Msun, where such signatures are found in ~ 50% of H$_2$-rich early-type galaxies. Our data are thus consistent with a scenario in which fast rotator early-type galaxies are quenched former spiral galaxies which have undergone some bulge growth processes, and in addition, some of them also experience cold gas accretion which can initiate a period of modest star formation activity. We discuss implications for the interpretation of colour-magnitude diagrams.