This paper presents two experiments on the processing of informative definite descriptions in plausible vs. implausible contexts. Experiment 1 is a self-paced reading task (with French native speakers, n = 69), with sentences containing a definite vs. indefinite NP, each preceded by plausible or implausible contexts. Our study replicated Singh and colleagues’ findings, namely that definite descriptions are significantly costlier when they occur in implausible contexts. The translation of the original stimuli from English to French did not affect the results, suggesting that the phenomenon applies cross-linguistically. Experiment 2 consists in an eye-tracking task, designed to measure the participants’ (n = 44) gaze patterns on complete sentences with the same four conditions (definite vs. indefinite NP; implausible vs. implausible contexts). A mixed effect model analysis revealed that (a) the total gaze duration on target segments and (b) the processing of the complete sentence were significantly longer in implausible conditions. These results show that implausible contexts predict a marked increase in the offline processing costs of definite descriptions. However, no significant difference was found for online processing measures (i.e., first fixation duration, first-pass reading time and regression path time measures) across all experimental conditions. These results suggest that it is only once the sentence is fully processed that implausible contexts increase processing costs. Furthermore, these results raise methodological issues related to the study of the online processing of definite descriptions, to the extent that self-paced reading and eye-tracking methods in the present study lead to incompatible results. With respect to the eye-tracking results, we suggest that the contrast between online and offline processing is likely to reflect the fact that participants first adopt a stance of trust to understand utterances before filtering the information through their epistemic vigilance module.