There is growing interest in selective breeding of the honeybee, resulting in the emergence of new breeding projects, often with an emphasis on improving resilience traits, in particular toward brood diseases. Lately, feed autonomy is also gaining importance. Here, we use data from a small breeding nucleus in France to estimate genetic parameters for common bee breeding traits and a novel trait reflecting honey reserves in the brood chamber. Open-mated queens were produced each year from inseminated dams between 2019 and 2021, and ~330 colonies were phenotyped each following year at three periods during the entire beekeeping season. Genetic parameters were estimated using ReML with an animal model. Narrow-sense heritability estimates ranged from low (around 0.15) for calmness and total capped brood surface both measured in early summer, to moderate (0.30 to 0.40) for hygienic behavior in spring, honey yield, and phoretic V. destructor load in early summer. Honey reserves in the brood chamber showed an intermediate heritability throughout the season (around 0.25). Gentleness had a null heritability. Most correlations between phenotypes adjusted for environmental fixed effects were close to zero. Among exceptions, there were honey reserves in the brood chamber in early summer with honey yield (around −0.2) and with the total capped brood surface in early summer (around −0.3). These estimates, although uncertain due to the dataset size, suggest that selection for production and resilience will be effective, even though simultaneous selection for honey yield and feed reserves might be difficult due to a possible genetic antagonism between both traits.