  Entanglement between photons at telecommunication wavelengths and long-lived
quantum memories is one of the fundamental requirements of long-distance
quantum communication. Quantum memories featuring on-demand read-out and
multimode operation are additional precious assets that will benefit the
communication rate. In this work we report the first demonstration of
entanglement between a telecom photon and a collective spin excitation in a
multimode solid-state quantum memory. Photon pairs are generated through widely
non-degenerate parametric down-conversion, featuring energy-time entanglement
between the telecom-wavelength idler and a visible signal photon. The latter is
stored in a Pr$^{3+}$:Y$_2$SiO$_5$ crystal as a spin wave using the full Atomic
Frequency Comb scheme. We then recall the stored signal photon and analyze the
entanglement using the Franson scheme. We measure conditional fidelities of
$92(2)\%$ for excited-state storage, enough to violate a CHSH inequality, and
$77(2)\%$ for spin-wave storage. Taking advantage of the on-demand read-out
from the spin state, we extend the entanglement storage in the quantum memory
for up to 47.7~$\mu$s, which could allow for the distribution of entanglement
between quantum nodes separated by distances of up to 10 km.
