  In this paper, we rewrite the time-dependent Bogoliubov$\unicode{x2013}$de
Gennes equation in an appropriate semiclassical form and establish its
semiclassical limit to a two-particle kinetic transport equation with an
effective mean-field background potential satisfying the one-particle Vlasov
equation. Moreover, for some semiclassical regimes, we obtain a higher-order
correction to the two-particle kinetic transport equation, capturing a
nontrivial two-body interaction effect. The convergence is proven for $C^2$
interaction potentials in terms of a semiclassical optimal transport
pseudo-metric. Furthermore, combining our current results with the results of
Marcantoni et al. [arXiv:2310.15280], we establish a joint semiclassical and
mean-field approximation of the dynamics of a system of spin-$\frac{1}{2}$
Fermions by the Vlasov equation in some negative order Sobolev topology.
