In this work, we consider a Fog Radio Access Network (F-RAN) system with a partially connected wireless topology and no channel state information available at the cloud and Edge Nodes (ENs). An F-RAN consists of ENs that are equipped with caches and connected to the cloud through fronthaul links. We first focus on the case where cloud connectivity is disabled, and hence the ENs have to satisfy the user demands based only on their cache contents. For a class of partially connected regular networks, we present a delivery scheme which combines intra-file MDS coded caching at the ENs and blind interference avoidance on the wireless edge channel. This scheme requires minimum storage and leads to an achievable Normalized Delivery Time (NDT) that is within a constant multiplicative factor of the best known NDT with full storage. We next provide achievable schemes for the case where cloud connectivity is enabled, and we provide new insights on the interplay between cloud connectivity and edge caching when only topological information is available.