Cross-cultural comparison of psychological meaning requires methods that go beyond word-level translation and examine how semantic dimensions are organized across languages. We introduce a cross-lingual extension of the Supervised Semantic Differential (SSD), which estimates supervised semantic gradients in embedding space and compares them across aligned multilingual word embeddings. The method tests gradient alignment and difference using permutation procedures and bootstrap intervals, and interprets residual differences through clustering around the difference gradient. We demonstrate the approach on Polish, English, and French affective norm lexicons, modeling Valence, Arousal, and Dominance where available. Affective dimensions were significantly recoverable across languages and model settings. Cross-lingual comparisons showed broad alignment together with structured residual differences: Valence appeared mostly shared, whereas Arousal and Dominance produced more interpretable contrasts involving bodily threat, aesthetic stimulation, internal emotionality, macro-level authority, and everyday control. Several clusters also reflected corpus-specific artifacts, underscoring the need for cautious interpretation. Cross-lingual SSD offers an explainable framework for testing semantic alignment, identifying divergence, and generating hypotheses about cross-cultural differences in psychological meaning.