We consider a Fog Radio Access Network (F-RAN) with a Base Band Unit (BBU) in the cloud and multiple cache-enabled enhanced Remote Radio Heads (eRRHs). The system aims at delivering contents on demand with minimal average latency from a time-varying library of popular contents. Information about uncached requested files can be transferred from the cloud to the eRRHs by following either backhaul or fronthaul modes. The backhaul mode transfers fractions of the requested files, while the fronthaul mode transmits quantized baseband samples as in Cloud-RAN (C-RAN). The backhaul mode allows the caches of the eRRHs to be updated, which may lower future delivery latencies. In contrast, the fronthaul mode enables cooperative C-RAN transmissions that may reduce the current delivery latency. Taking into account the trade-off between current and future delivery performance, this paper proposes an adaptive selection method between the two delivery modes to minimize the long-term delivery latency. Assuming an unknown and time-varying popularity model, the method is based on model-free Reinforcement Learning (RL). Numerical results confirm the effectiveness of the proposed RL scheme.