I actually like the melody, which is a stirring march. I hear it almost every day when I get up. A couple of radio stations south of the border play it at six AM on weekdays. One plays a version by a brass band, and the other features a choir singing its bellicose lyrics.
Oddly enough, the melody was written not by a Mexican. Jaime Nunó, a Catalan born in Gerona, in the foothills of the Pyrenees, gained fame as a leader of bands in Spain and Cuba before being invited by Mexican president Antonio López de Santa Anna to come to Mexico to lead military bands. It was during his brief time in Mexico, in 1854, that he wrote the melody to the anthem. Shortly afterwards, Santa Anna was ousted, and Nunó immigrated to the United States, settling in New York.
Listen to the Mexican national anthem here.
The Pyrenees are in the Basque country, not in Catalonia.