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Local authorities actively advocate for cycling as a pivotal mode to shift urban transportation towards greater sustainability. Weather significantly influences bicycle traffic and may hinder the spread of bicycle adoption, potentially limiting its impact to mitigate climate change. Likewise, rising temperatures and extreme weather events are anticipated to influence mobility patterns. To better understand the complex effects of weather on bicycle traffic, an explainable artificial intelligence analysis is carried out on four territories in France. Employing a neural network, we model the effects of weather conditions and control variables (e.g., pollution) on bicycle traffic. Subsequently, we examine the marginal effects of each variable using Accumulated Local Effects plots. Based on this analysis, we formulate a nonlinear model with seasonal autoregressive with moving-average errors. This analytical model encapsulates new equations describing the effects of weather conditions on bicycle traffic. The methodology combines the ability of black-box model to capture complex nonlinear relationships without prior assumptions, with the transparency and generalization capabilities of analytical models. It also highlights the asymmetric sensitivity of bicycle traffic to humidity, with humid conditions being more deterrent than dry conditions. Statistical analysis reveals that atmospheric pressure is significantly correlated to bicycle traffic, whereas air quality does not demonstrate notable effects, contrary to observations in other territories.