This study aimed to analyse the driver’s behaviour during the interaction with a pedestrian crossing into and outside the zebra crossing, and evaluate the effectiveness of two kinds of Advanced Driver Assistance System (ADAS) that provided to the driver an auditory alert, and a visual alert to detect the pedestrian. 42 participants joined the experiment conducted using the fixed-base driving simulator of the Department of Engineering (Roma Tre University). They experienced different crossing conditions (legal and illegal) and ADAS conditions (no ADAS, visual warning and auditory warning) in an urban scenario. The parameters Time-To-Arrive (TTA) and Speed Reduction Time (SRT) were obtained from the drivers’ speed profiles in the last 150 m in advance of the conflict point with the pedestrian. Results clearly showed the criticality of illegal crossings. When the pedestrian crossed outside of the crosswalk, the highest number of collision occurred and the ANalysis Of VAriance (ANOVA) returned significant effects on both the dependent variables TTA and SRT, highlighting the higher criticality of the vehicle–pedestrian interaction and the more abrupt yielding manoeuvre. Positive effects (the vehicle–pedestrian interaction was less critical and the yielding manoeuvre was smoother) emerged for both the driver assistance systems, although not statistically significant. Besides, both the driver assistance systems positively affected the behaviour of the average cautious drivers. No significant effects of the warning systems were recorded on the aggressive drivers, which because of their behavioural characteristics ignored the warning alarm. In addition, no significant effects of the warning systems were recorded for the very cautious drivers, which adjusted their behaviour even before the alarm trigger. Finally, the outcomes of the questionnaire submitted to the participants highlighted the clear preference for the auditory warning, probably because of the different physical stimuli that are solicited by the warning signal. The results confirm that adequate pedestrian paths should be planned to avoid jaywalker conditions, which induce the driver to assume critical driving behaviour and provide useful findings of the effectiveness of driver assistance systems for pedestrian detection.