In this event-related potential (ERP) study we reevaluate syntax-first approaches to sentence processing by implementing a novel paradigm in French that includes correct sentences, pure syntactic category violations, lexical-semantic anomalies, and combined anomalies. Our balanced design systematically controlled for target word (noun vs. verb) and the context immediately preceding it. Group results from 36 native speakers of Quebec French revealed that, up to 300 ms, ERPs elicited by syntactic category violations were comparable with ERP responses to correct sentences, showing that there is no early activation reflecting syntactic category identification. Instead, in response to all anomalous conditions, we observed an N400 followed by a P600. Combined anomalies yielded additive effects of syntactic category and lexical-semantic anomalies on the N400, and a large P600 effect similar to the one observed in the pure syntactic condition. These results provide strong evidence against the hypothesis that (i) syntactic categories are processed first, and (ii) that syntactic category errors "block" lexical-semantic processing. Further, the N400 effect in response to pure syntactic category violations reflects a mismatch detection between a predicted word-stem and the actual target. This mechanism takes place simultaneously (and potentially in parallel) with lexical-semantic processing. In contrast, an interaction of syntax and semantics for the P600 reveals that the same neurocognitive resources are recruited for syntactic and semantic integration, both promoted by the implementation of an acceptability judgement task in our design. Additional analyses of individual data complemented these observations: during sentence processing, participants did not rely on one single cognitive mechanism reflected by either the N400 or the P600 effect but on both, suggesting that the biphasic N400-P600 ERP wave can indeed be considered to be an index of phrase-structure violations in most individuals, at least if they are realized on content words.