The COVID-19 pandemic has led to widespread social isolation. This study aimed to determine anxiety levels among parents of school-aged children and investigate the associated factors. Data on sociodemographic characteristics, living and working conditions, family relationships, social support (MSPSS) and health status (SF-12) were collected from French parents through an online survey. The Generalized Anxiety Disorder Scale (GAD-7) was used to assess anxiety. Logistic regression analysis was performed to identify the factors associated with moderate to severe anxiety. Among 698 parents, 19.2% experienced moderate to severe anxiety. A low level of resilience (OR = 4.3, 95% CI: 2.7–6.7) and confirmed COVID-19 cases involving hospitalization (OR = 3.8, 95% CI: 2.0–7.3) among individuals in one’s household or in the family circle were found to be the main risk factors for moderate to severe anxiety. Other factors were also identified: a level of education less than high school (OR = 2.1, 95% CI: 1.3–3.2), conflicts at home (OR = 2.3, 95% CI: 1.4–3.7), noises outside the home (OR = 2.0, 95% CI: 1.0–3.9), confirmed cases not involving hospitalization (OR = 1.8, 95% CI: 1.0–3.1) and suspected cases (OR = 1.9, 95% CI: 1.0–3.8). Family support was a protective factor. These findings suggest some need for support programs to help parents cope with public health crises and work-family challenges.