Several risk factors of children’s mental health issues have been identified during the pandemic of COronaVIrus Disease first appeared in 2019 (COVID-19). This study aims to fill the knowledge gap regarding the association between parents’ and children’s mental health issues during the COVID-19 school closure in France. We conducted a cross-sectional analysis of data collected in the SAPRIS-ELFE study during the COVID-19 pandemic in France. Using multinomial logistic regressions, we estimated associations between parents’ and children’s mental health issues. Symptoms of anxiety were assessed by the General Anxiety Disorder-7 (GAD-7) and depression by the Patient Health Questionnaire-9 (PHQ-9) for the parents. Hyperactivity/inattention and emotional symptoms in children were assessed by the Strengths and Difficulties Questionnaire (SDQ). The sample included 3496 children aged 8 to 9 years, of whom 50.0% were girls. During the school closure, 7.1% of responding parents had moderate to severe levels of anxiety and 6.7% had moderate to severe levels of depression. A total of 11.8% of the children had an abnormal hyperactivity/inattention score and 6.6% had an abnormal emotional symptoms score. In multivariate regression models, parental moderate to severe level of anxiety and moderate to severe level of depression were associated with abnormal hyperactivity-inattention score (adjusted Odds Ratio (aOR) 3.31; 95% Confidence Interval (CI) 2.33–4.70 and aOR 4.65; 95% CI 3.27–6.59, respectively) and abnormal emotional symptoms score in children (aOR 3.58; 95% CI 2.33–5.49 and aOR 3.78; 95 CI 2.47–5.78 respectively). Children whose parents have symptoms of anxiety and/or depression have an increased likelihood of symptoms of hyperactivity/inattention and emotional symptoms during school closures in France due to COVID-19. Our findings suggest that public health initiatives should target parents and children to limit the impact of such crises on their mental health issues.