Frederick. The middle names don't really matter.
p.s. I would like it to be John or James, but neither of those is 'pre-Regency', 'Regency', or modern Anglo-Germanic.
Update: Hmm, I never even considered Louis (pronounced Lou-ee, we are told -- not the usual English Lou-iss). Not that I gave it much thought, to be honest. A two-syllable name might have been preferred, though it must be said that the third one of 'Frederick' is awfully quick. Louis is a little outside the mould, but I didn't lay any money down so that's all right!
Update, Friday night: Definitely not keen on 'Louis'. I've long thought it a bore when reading about French kings (186 years of the same king name: talk about stuck in a rut!). Also, when not used by French kings, it strikes me as distinctly un-aristocratic, even anti-aristocratic. Think about it: Lou Reed of the Velvet Underground. Lou Grant (fictional character) of The Mary Tyler Moore Show. Louis Farrakhan. I know that the royal family's associations are more positive, but I think those associations are overdone, quite frankly. Nope, I would have preferred almost anything else. Oh well.