We present a high spatial resolution (~ 14 x 11 pc^2) ALMA CO(J=3-2) map of the nearby fast-rotating early-type galaxy NGC4429. We use our modified CPROPStoo code to identify and characterise 217 giant molecular clouds (GMCs) within the 450 pc radius of the molecular gas disc. The GMCs generally have a smaller size, lower mass, higher velocity dispersion and similar mass surface density than the GMCs in the Milky Way and Local Group galaxies. The cloud mass function has a steep slope (index <-2) with a cut off at ~ 9 x 10^5 Msolar. An unusually steep size-line width relation and high internal cloud velocity gradients (0.12 - 0.36 km/s /pc) are found, that may be due to cloud-scale gas motions driven by the background galactic gravitational potential (i.e. local circular motions in the disc). We thus revisit the conventional Virial theorem and define an effective Virial parameter, α_eff,vir, to take into account the effect of the background gravitational potential. The NGC4429 clouds then appear to be gravitationally unbound  (<α_eff,vir>= 2.15 +/- 0.06 or< α_eff,vir>~2.3 - 3.2 if the cloud shapes are considered), due to the strong effects of galactic shear and tidal forces. We also find the clouds have enclosed stellar masses a factor ~6 larger than their gas masses and radii larger than their predicted Roche radii, further suggesting that they are not gravitationally bound. Lastly, we observe a trend of cloud properties with galactocentric radius, that seems driven by the decreasing external pressure and galactic rotational shear with increasing radius. The mass surface density appears to be regulated by the external pressure, while the size (or mass) seems to be determined by the galactic rotational shear.