(1) Background: Climate change is a major threat to human health and new research is highlighting its effects on physical health. However, there is still little research on the psychological effects, particularly on young people, who seem to be disproportionately affected. (2) Objectives: In this context, we conducted a study focusing on the young adult population to identify psychosocial and behavioral factors that may modulate the intensity of this anxiety. (3) Method: A cross-sectional study by questionnaire was carried out on a sample of 369 young French adults. Data were analyzed via structural equation modelling. (4) Results: The main results suggest that: (1) CFC and information seeking predict climate anxiety, which in turn predicts the emotional consequences of exposure to information about the negative consequences of climate change; (2) information seeking moderates the effects of CFC on climate anxiety. (5) Conclusions: This study highlights both the role of temporal orientation and information seeking on the climate anxiety experienced by young adults. These results provide an interesting lever for health professionals to work with this population who may be more vulnerable to climate anxiety than others.