How the brain supports language across different languages is a basic question in neuroscience and a useful test for multilingual artificial intelligence. Neuroimaging has identified language-responsive brain regions across languages, but it cannot by itself show whether the underlying processing is shared or language-specific. Here we use six multilingual large language models (LLMs) as controllable systems and create targeted ``computational lesions'' by zeroing small parameter sets that are important across languages or especially important for one language. We then compare intact and lesioned models in predicting functional magnetic resonance imaging (fMRI) responses during 100 minutes of naturalistic story listening in native English, Chinese and French (112 participants). Lesioning a compact shared core reduces whole-brain encoding correlation by 60.32% relative to intact models, whereas language-specific lesions preserve cross-language separation in embedding space but selectively weaken brain predictivity for the matched native language. These results support a shared backbone with embedded specializations and provide a causal framework for studying multilingual brain-model alignment.