AmourShipping is the belief that Ash and Serena belong in a romantic relationship. The name is derived from the French word "amour", meaning "love". It was chosen as the name because the Kalos region is inspired by France (known for its romantic atmosphere) and Serena has a canonical crush on Ash.
AmourShipping is one of the most popular ships in the Pokemon pairings that involves two adults. It is extremely well-known, because of Serena's canon crush on Ash. Many fans think that Ash will catch on at some point and return the love to Serena.