Cross-lingual topic modeling aims to uncover shared semantic themes across languages. Several methods have been proposed to address this problem, leveraging both traditional and neural approaches. While previous methods have achieved some improvements in topic diversity, they often struggle to ensure high topic coherence and consistent alignment across languages. We propose XTRA (Cross-Lingual Topic Modeling with Topic and Representation Alignments), a novel framework that unifies Bag-of-Words modeling with multilingual embeddings. XTRA introduces two core components: (1) representation alignment, aligning document-topic distributions via contrastive learning in a shared semantic space; and (2) topic alignment, projecting topic-word distributions into the same space to enforce cross-lingual consistency. This dual mechanism enables XTRA to learn topics that are interpretable (coherent and diverse) and well-aligned across languages. Experiments on multilingual corpora confirm that XTRA significantly outperforms strong baselines in topic coherence, diversity, and alignment quality.