Stance detection aims to determine the stance of a text towards a specific target. Most research focuses on a single language with limited targets. Zero-shot cross-lingual stance detection addresses linguistic resource imbalances by training models on English datasets to predict stances in low-resource languages. However, existing studies overlook differences in stance reasoning across languages. To tackle this, we introduce a novel Multilingual Inference Paradigm in zero-shot cross-lingual Stance detection (MIPS). Our approach integrates target and language adaptation while accounting for the reasoning relationships between texts and targets across languages. Specifically, we leverage large language models (LLMs) to expand domain knowledge for stance reasoning and employ windowed feature extractors to capture diverse expression structures across languages. Moreover, we align reasoning relationships between texts in different languages and the same target through contrastive learning. Comprehensive evaluations on 10 datasets in 7 languages from 5 language families demonstrate that MIPS outperforms current stance detection baselines.