Multilingual machine translation models must adapt to the grammatical structure of the target language, yet how structural information shapes decoder computation remains unclear. Using the eigenvalue spectra of per-(layer, head) attention Gram matrices instead of raw attention weights, we show that cross-attention geometry in NLLB-200 is organized around the target language: these spectral features carry a strong, distributed signal about target-language word order (SVO vs. SOV) when English is the source, with near-perfect decodability across cross-validation. The signal is not concentrated in a small subset of heads, but is broadly distributed across layers and heads—yet it degrades sharply at every level of aggregation when English is the target. This asymmetry suggests that cross-attention geometry reflects the demands of target-side generation rather than source-side structure. Leave-one-language-out evaluation confirms that the signal generalizes to unseen languages, ruling out language identity as a confound.