  We construct a Connes spectral triple or `Dirac operator' on the non-reduced
fuzzy sphere $C_\lambda[S^2]$ as realised using quantum Riemannian geometry
with a central quantum metric $g$ of Euclidean signature and its associated
quantum Levi-Civita connection. The Dirac operator is characterised uniquely up
to unitary equivalence within our quantum Riemannian geometric setting and an
assumption that the spinor bundle is trivial and rank 2 with a central basis.
The spectral triple has KO dimension 3 and in the case of the round metric,
essentially recovers a previous proposal motivated by rotational symmetry.
