As with any other medications, there is the chance that naproxen sodium and alcohol can interact. In general it is not a good idea to take most pain medications including NSAIDs with alcohol.
Taking naproxen increases the risk of damage to the lining of the stomach. The reason is because this drug reduces the production of a compound that protects this lining.
Drinking alcohol while taking naproxen can cause further damage. After all, alcohol is an irritant. So, the reduction in the protection to stomach lining allows the alcohol to cause irritation. This irritation can lead to heartburn or more serious issues like a bleeding ulcer. Alcohol also thins the blood, and if an ulcer were to develop as a result of taking both naproxen and alcohol that can lead to an even more serious ulcer.