We introduce the Cluster-EAGLE (c-eagle) simulation project, a set of cosmological hydrodynamical zoom simulations of the formation of 30 galaxy clusters in the mass range of 1014 < M200/M⊙ < 1015.4 that incorporates the Hydrangea sample of Bahé et al. (2017). The simulations adopt the state-of-the-art eagle galaxy formation model, with a gas particle mass of 1.8 × 106 M⊙ and physical softening length of 0.7 kpc. In this paper, we introduce the sample and present the low-redshift global properties of the clusters. We calculate the X-ray properties in a manner consistent with observational techniques, demonstrating the bias and scatter introduced by using estimated masses. We find the total stellar content and black hole masses of the clusters to be in good agreement with the observed relations. However, the clusters are too gas rich, suggesting that the active galactic nucleus (AGN) feedback model is not efficient enough at expelling gas from the high-redshift progenitors of the clusters. The X-ray properties, such as the spectroscopic temperature and the soft-band luminosity, and the Sunyaev-Zel'dovich properties are in reasonable agreement with the observed relations. However, the clusters have too high central temperatures and larger-than-observed entropy cores, which is likely driven by the AGN feedback after the cluster core has formed. The total metal content and its distribution throughout the intracluster medium are a good match to the observations.