  Solid-state atomic defects with optical transitions in the telecommunication
bands, potentially in a nuclear spin free environment, are important for
applications in fiber-based quantum networks. Erbium ions doped in CeO$_2$
offer such a desired combination. Here we report on the optical homogeneous
linewidth and electron spin coherence of Er$^{3+}$ ions doped in CeO$_2$
epitaxial film grown on a Si(111) substrate. The long-lived optical transition
near 1530 nm in the environmentally-protected 4f shell of Er$^{3+}$ shows a
narrow homogeneous linewidth of 440 kHz with an optical coherence time of 0.72
$\mu$s at 3.6 K. The reduced nuclear spin noise in the host allows for
Er$^{3+}$ electron spin polarization at 3.6 K, yielding an electron spin
coherence of 0.66 $\mu$s (in the isolated ion limit) and a spin relaxation of
2.5 ms. These findings indicate the potential of Er$^{3+}$:CeO$_2$ film as a
valuable platform for quantum networks and communication applications.
