Screen time among children in most European countries is notably high and is influenced by various sociodemographic and other factors. Our study aimed to explore the associations between parents’ sociodemographic characteristics, socioeconomic status, body mass index (BMI), physical activity, risk status for type 2 diabetes, and their children’s BMI, physical activity, and screen time. The data were sourced from the 2016 Feel4Diabetes study, involving 12,280 parents and 12,211 children aged 6–9 years (average age 8.21 years) in a cross-sectional study design. We used a logistic regression model to identify potential factors associated with children’s screen time. The results showed that mothers with tertiary education (OR = 0.64; 95%CI = 0.49–0.82; p < 0.001), the middle age group (45–54 years) (OR = 0.81 95%CI = 0.66–0.98; p = 0.033), and families with higher incomes (middle–OR = 0.85; 95%CI = 0.75–0.97; p = 0.014; high–OR = 0.8; 95%CI = 0.69–0.93; p = 0.003) were associated with a decreased chance of children spending more than 2 h/day in front of the screen. In contrast, maternal overweight/obesity (OR = 1.15; 95%CI = 1.03–1.29; p = 0.013) and lower physical activity in children were linked to an increased likelihood of more than 2 h of screen time per day. Our findings suggest that targeted interventions should be developed to mitigate excessive screen time, particularly focusing on low-income families and mothers with low educational levels.