In the current context of climate change, agroforestry systems are acknowledged to have a good potential to increase carbon storage in agricultural areas. However, the carbon storage potential of agroforestry systems still needs to be quantified accurately, especially for hedges. The objectives of this study were to (1) add references to the existing literature on the potential for soil organic carbon (SOC) storage near hedges and (2) identify the main factors that influence the variability in this potential. To this end, we sampled soil in the adjacent fields of 25 hedges in France with mixed crop-livestock agriculture, with sampling on both sides for 20 hedges and sampling on only one side for 5 hedges, giving a total of 45 study sites. We measured SOC stocks to a depth of 90 cm at distances of 1, 2, 3, and 10 m from the hedge. The results showed that hedges have a strong potential to store carbon in soils, with a mean increase of 15% in SOC stock within 3 m of the hedge. This increase in SOC stock had high variability due to site characteristics. Additional SOC stocks were the largest in rotations of annual crops and grasslands with a permanent grass strip 1 m wide near the hedge, followed by rotations of annual crops, permanent grasslands, and rotations of annual crops and grasslands. Large additional SOC stocks due to the hedge were also associated with soils that had a high C:N ratio. The contribution of this type of land management to soil carbon storage thus depends on the local context in which it is implemented.