The urgency of the climate crisis emphasizes the importance of reducing greenhouse gas emissions, a goal that cities intend to achieve by developing their cycling infrastructure. However, sustainability includes social equity, and transport has been shown to play a role in reinforcing urban inequalities. This study seeks to understand how cycling infrastructure can be developed to reduce greenhouse gas emissions and urban inequalities by assessing emerging equity-induced trade-offs in prioritizing cycling projects within the Grand Paris Metropolis, France. By combining automated identification of cycling infrastructure gaps with equity frameworks, this research identifies shifts in the prioritization of infrastructure projects based on degrees of equity emphasis. The focus lies on vulnerable populations, specifically children commuting to school coming from neighborhoods with lower educational attainment and adults commuting to work from neighborhoods with lower median income. The outcomes reveal that introducing equity considerations impacts the order of importance of infrastructure projects, though the overall trajectory remains intact, suggesting that integrating equity into transport planning is an achievable goal.