Understanding how accessibility shapes participation in leisure activities is central to promoting inclusive and vibrant urban life. Conventional accessibility measures often focus on potential access from fixed home locations, overlooking the constraints and opportunities embedded in daily routines. In this study, we apply a space-time accessibility (STA) metric rooted in the capability approach, capturing feasible leisure opportunities between home and work given a certain time budget, individual transport modes, and urban infrastructure. Using high-resolution GPS data from 2,415 working residents in the Paris region, we assess how STA influences leisure participation during weekdays, measured as the diversity of leisure locations visited and activity duration. Observed destination choices confirm that most individuals select leisure locations within their STA-defined opportunity sets, validating the metric as a proxy for capability sets. Structural equation modeling shows that STA exerts a significant positive total effect on leisure participation ($β= 0.14$, $p < .001$), driven by a significant direct effect ($β= 0.18$, $p < .001$) that is only modestly offset by an indirect pathway through reduced travel time ($β= -0.04$, $p < .01$). Individual attributes also directly shape participation: active mode use and higher education promote leisure engagement, while local poverty and caregiving responsibilities constrain it. These findings highlight the value of person-centered, capability-informed accessibility metrics for understanding inequalities in urban mobility and informing transport planning strategies that expand real freedoms to participate in social life across diverse population groups.