A new experimental paradigm is proposed to examine and collate the presence of an exhaustive inference in English it-clefts and French c'est-clefts. A pragmatic account of the contrasts between English and French is presented related to the way the existential presupposition derived from the cleft structure interacts with context. English and French clefts diverge as to the strength with which they express exhaustivity, both in offline and online measures. English clefts are exhaustive by default but French clefts are not.