A Fog Radio Access Network (F-RAN) is a cellular wireless system that enables content delivery via the caching of popular content at edge nodes (ENs) and cloud processing. The existing information-Theoretic analyses of F-RAN systems, and special cases thereof, make the assumption that all requests should be guaranteed the same delivery latency, which results in identical latency for all files in the content library. In practice, however, contents may have heterogeneous timeliness requirements depending on the applications that operate on them. Given per-EN cache capacity constraint, there exists a fundamental trade-off among the delivery latencies of different users' requests, since contents that are allocated more cache space generally enjoy lower delivery latencies. For the case with two ENs and two users, the optimal latency trade-off is characterized in the high-SNR regime in terms of the Normalized Delivery Time (NDT) metric. The main results are illustrated by numerical examples.