Pseudo-cleft-like structures in Hebrew and French conversation: The syntax-lexicon-body interface

•Heb. ma she- / Fr. ce que clauses in pseudo-clefts are projecting constructions.•They show strong lexico-semantic, syntactic, and prosodic consistencies.•They project reports of actions/events, paraphrases, displays of speaker’s stance.•They serve as attention-getting devices at the opening of a new sequence/episode.•Speaker’s prominent embodied conduct furthers their attention-getting function.•The two languages show different degrees of grammaticization of the constructions.