Content Delivery Networks (CDNs) are a key enabler for the distribution of large amounts of data with high capacity and low latency. For instance, content streaming companies extensively use geographical distribution and replication to meet the ever-growing demand for media. Optical networks are the only future-proof technology available that meets the reach and capacity requirements of CDNs. However, the robustness of optical networks becomes a point of concern, as they can be a target of deliberate link cuts that can severely degrade network connectivity and cause large-scale service disruption. To mitigate the vulnerabilities, actions can be taken in the optical and/or cloud infrastructures. The replication of content across geographically diverse data centers results in an intrinsic increase of content accessibility. At the network infrastructure level, robustness to attacks can be enhanced by increasing the topology connectivity through link addition. This work focuses on the latter approach and its effectiveness in increasing content accessibility in the presence of deliberate link cuts. The paper proposes a framework for evaluation and enhancement of content accessibility in CDNs by sparse link addition. First, a content accessibility measure called mu-ACA is introduced to gauge the content accessibility of a given network topology under a set of link cut attack scenarios. Based on this measure, a new link addition strategy is defined aimed at maximizing the content accessibility for a given number of extra links. Simulation results on real-world reference topologies show that the proposed strategy can significantly improve content accessibility by adding a very limited number of optical fiber links.