Strong interaction between single atoms and photons via cavity quantum electrodynamics has been applied many times, including first demonstrations of quantum networks. However, the small optical resonators of high finesse used there make scaling of quantum networks very challenging. Here, we present experimental results on an alternative approach using a concentric cavity. The tightly focused mode leads to strong atom-photon interaction at a macroscopic cavity length, while relaxing demands for a high finesse. This is also relevant for many quantum systems, in particular for ions and Rydberg atoms which are difficult to incorporate in small cavities.