Weird Al has always been a serious musician; I've admired the guy's work for 30 years, and to me it was always apparent. He's known for his parodies of popular songs, but a lot of his songs are just silly fun songs, with an odd bent towards food as a subject. There are also Polka versions of songs. "Bohemian Polka" is not really a parody; it's just the song done in a different style.
Then there are the "style parodies", which are meant to ape the style and sound of a particular band or artist, but not a specific song. "Mr. Popeil" is clearly a B-52's style parody. "When I Was Your Age" is obviously Don Henley. That kind of thing. Also, Al never comes out and says who the subject is. That's up to us to figure out. But in everything, the level of detail and the dedication to true satire and parody is apparent. I was not surprised at all to learn that he comes from a musical family and has a genius IQ.
I consider "Genius in France" somewhat unique. It's definitely from the "style parody" mold, but also a genuine tribute to someone Al truly admired. Since Frank didn't have a single, defineable sound, but did have a number of musical trademarks in his catalog, Al was challenged to incorporate as many as he could. I think he succeeded. Also, it's true that Frank never really reached the level of honor and respect here in the U.S. that he did in France. In France, there are statues of him.
It's also possible that the song is slightly meant to whine a bit about Al himself never getting the true respect as an artist that he feels he deserves, but that might be stretching it a bit. Al knows he's in a niche, and he's done very, very well.