  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 $10^{14}<M_{200}/\mathrm{M}_{\odot}<10^{15.4}$ that
incorporates the Hydrangea sample of Bah\'e et al. (2017). The simulations
adopt the state-of-the-art EAGLE galaxy formation model, with a gas particle
mass of $1.8\times10^{6}\,\mathrm{M}_{\odot}$ and physical softening length of
$0.7\,\mathrm{kpc}$. 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 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 ICM are a good match to the observations.
