Background: The COVID-19 pandemic placed important challenges on parents, as they had to meet various demands during lockdown, including childcare, work and homeschooling. Therefore, the current study aimed to investigate perceived stress levels among the parents of school-aged children and explore their association with sociodemographic, environmental and psychological factors during lockdown. Methods: A cross-sectional study was conducted among the parents of school-aged children ages 8 to 18, who lived in the Grand Est region of France during the first wave of the pandemic. An online survey collected sociodemographic data, living and working conditions, and exposure to COVID-19 as well as parent’s levels of perceived stress (PSS-10), self-perceived health status (SF-12), social support (MSPSS) and resilience (BRS). Multivariable logistic regression models were conducted to evaluate the association between moderate to severe perceived stress and various factors. Results: In total, 734 parents were included. The results indicated that 47% were experiencing moderate stress and 7.2% were experiencing severe stress. Factors most strongly associated with risk of moderate to severe levels of stress were lower levels of parental resilience (OR = 3.8, 95% CI: 2.2–6.6) and poor self-perceived mental health status (OR = 7.3, 95% CI: 5.0–10.8). The following risk factors were also identified: female sex; being in the age range of 35–44; difficulties isolating and contracting COVID-19, which involved hospitalization and separation or isolation from family. The support of friends (OR = 0.8, 95% CI: 0.7–1.0) and family (OR = 0.5, 95% CI: 0.3–0.8) were protective factors. Conclusions: These findings suggest that supportive and preventive programs should focus on the improvement of resilience and mental health management to promote parents’ wellbeing. Research has to focus both on individuals’ inner potential for increasing resilience and the environmental resources to be activated. Building and boosting resilience among parents could serve as a protective factor against negative outcomes for them and their families.