  Given a compact metric space X and a unital AF algebra A equipped with a
faithful tracial state, we place quantum metrics on the tensor product of C(X)
and A given established quantum metrics on C(X) and A from work with Bice and
Latr\'emoli\`ere. We prove the inductive limit of C(X) tensor A given by A is a
metric limit in the Gromov-Hausdorff propinquity. We show that our quantum
metric is compatible with the tensor product by producing a Leibniz rule on
elementary tensors and showing the diameter of our quantum metric on the tensor
product is bounded above the diameter of the Cartesian product of the quantum
metric spaces. We provide continuous families of C(X) tensor A which extends
our previous results with Latr\'emoli\`ere on UHF algebras.
