Though activation of Broca’s region in the combinatorial processing of symbols (language, music) has been revealed by neurometabolic studies, most previous neurophysiological research found the earliest grammar indices in the temporal cortex, with inferior-frontal generators becoming active at relatively late stages. We use the attention- and task-free syntactic mismatch negativity (sMMN) event-related potential (ERP) to measure rapid and automatic sensitivity of the human brain to grammatical information in participants’ native language (French). Further, sources underlying the MMN were estimated by applying the Parametrical Empirical Bayesian (PEB) approach, with the Multiple Sparse Priors (MSP) technique. Results showed reliable grammar-related activation focused on Broca’s region already in the 150–190 ms time window, providing robust documentation of its involvement in the first stages of syntactic processing.