Full Event Interpretation is an algorithm for tag-side $B$ meson reconstruction at Belle II. The algorithm employs a hierarchical reconstruction of exclusive decay chains of $B$ mesons, with multivariate classifiers utilised to identify each unique sub-decay channel. Here, calibration factors are derived for hadronic tag-side $B$ decays by measuring $B \rightarrow X\ell \nu$ decays. For a very loose selection on the tag-side $B$ multivariate classifier, the calibration factors are $0.65 \pm 0.02$ and $0.83 \pm 0.03$ for tag-side $B^{+}$ and $B^{0}$ mesons, respectively. The calibrated hadronic tag-side decay modes are used to measure the branching fractions $\mathcal{B}(B^{0} \rightarrow D^{*+} \ell^{-} \bar{\nu}_{\ell}) = (4.45 \pm 0.41 ({\rm stat}) \pm 0.27 ({\rm sys}) \pm 0.45 (\pi_{\rm s})) \times 10^{-2}$ and $\mathcal{B}(B^{0} \rightarrow \pi^{+} \ell^{-} \bar{\nu}_{\ell}) = (1.62 \pm 0.42 ({\rm stat}) \pm 0.07 ({\rm sys})) \times 10^{-4}$ in $34.6$ fb$^{-1}$ of Belle II data.