In laying hen production, cage-free housing is growing rapidly to provide living conditions that meet hens’ needs. Unlike cages, this housing requires nests for automatic collection of eggs, as eggs laid outside nests must be collected by hand. Selecting hens for nest-related traits, such as egg production in nests and nesting behaviour, could help meet the requirements of cage-free housing. However, genetic correlations between these traits and major traits of breeding programmes, such as egg quality or BW, are poorly known. In addition, the genetic determinism of major traits has rarely been studied under cage-free conditions. The objective of the present study was to estimate the heritability of egg quality and BW measured on the floor and their genetic correlations with nest-related traits. Egg production in nests was based on the laying rate in nests, laying rhythm (clutch number and mean oviposition time), and nest acceptance. Nesting behaviour was based on nest preference (mean distance between nests used for laying) and mean laying duration (time spent in the nest for laying). Nest-related traits were recorded from 24 to 64 weeks of age. BW and egg quality were measured at 50 and 55 weeks of age, respectively. Nest-related traits and identification of the eggs laid by each hen (for individual measurements of egg quality) were obtained using individual electronic nests used by hens raised in groups and on the floor. The phenotypes of 1 455 Rhode Island Red and 1 538 White Leghorn hens were analysed. Heritability coefficients and genetic correlations were estimated using a multi-trait animal model for each line. Heritability estimates for egg quality and BW were moderate to high for both lines (0.17–0.74). Overall, weak genetic correlations were estimated between nest-related traits and egg quality or BW for both lines. However, strong and antagonistic genetic correlations were estimated between eggshell strength and laying rate in the nests (−0.46 to −0.42) or laying rhythm (+0.46 to +0.68) for both lines. Several moderate-to-strong genetic correlations were found for White Leghorn between nest-related traits and egg weight, eggshell shape, albumen height, and BW. This study shows that nest-related traits can be used to select hens better adapted to cage-free housing without degrading overall egg quality and BW. It also shows that some traits, like the eggshell strength, must be carefully monitored if these new traits are included in breeding goals. These results must now be confirmed for other populations and larger datasets.