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The socioeconomic and built environment of an area are interrelated with health data and have a direct influence on children’s development. There are facilitators and barriers for schools to promote physical activity depending on the socioeconomic status of the school. The aim of this study was to analyse the relationship between physical activity and sleep and the socioeconomic level of children in the Basque Country. The sample consisted of 1139 schoolchildren between the ages of six and seventeen (566 boys and 573 girls) from 75 schools (43 public and 32 private). Differences between groups were compared using the Mann–Whitney U test (two samples), Kruskal–Wallis one-factor ANOVA (k samples), and Spearman’s Rho correlation. There are sex differences in light (200.8 ± 62.5 vs. 215.9 ± 54.7) and moderate (69.0 ± 34.3 vs. 79.9 ± 32.1) physical activity in favour of the female group of higher socioeconomic status compared to male group of higher socioeconomic status. In the case of vigorous physical activity, the female group performed less than the male group across all socioeconomic statuses, which was statistically significant in the groups of high socioeconomic status (11.6 ± 9.3 vs. 6.9 ± 5.7) in group 2 and medium socioeconomic status (11.1 ± 9.3 vs. 7.7 ± 6.1) in group 3. There is an inverse relationship between sedentary behaviour and BMI, total bed time, total sleep time, and night-time awakenings. There is also an inverse relationship between all levels of physical activity performed with respect to BMI and total sleep efficiency. These data point towards notable inequalities in physical activity and daily sleep in Basque schoolchildren, which in turn may be marginalised in our current school system due to the effects of the socioeconomic environment.