Okay, I'm pretty sure I've figured out the last bit, but I'm trying to figure out the first half.
Wild guess here: Considering the latter clues strongly suggest a golf course near the palace of Versailles in France (More than likely the 12th hole of the Golf Des Yvelines, which was the first golf course in France), I'm guessing the "country's prime" refers to a king, probably King Louis the XIII, since 13 is a prime number. Additionally, Louis the XIII was the king in Alexander Dumas book "The Three Musketeers". The "detective" line could refer to the book's sequel "Man in the Iron Mask", wherein the titular man is a son of Louis the XIII, hidden in a prison.
"Sweet Spot" refers to a manner hitting a golf ball in just the perfect manner.
Anyway, my guesses.
Although cool, I think you might have the same misunderstanding as ashersky had. The goal is not to solve the riddle and guess where the image is, the goal is to
find the image in google maps. Looking over the Golf Des Yvelines, I cannot find this image...thus it isn't the correct answer (or I just didn't find it, which is possible)
However, this is a golf course, and likely the 12th is intended to guide us to that. (I don't know how golf courses are laid out, maybe 12th will direct us to the very image for someone who knows it).
It appears to me that gold courses look the same the world over, so I think we really need to solve the first bit to get anywhere.
It used to take a detective to find this country's prime.My wife suggested that it could be the prime minister.
A google search for Prime Minister Watson turned up Australia. But I don't see any "sweet spot"s there. And a search for antionette didn't turn up anything useful. Any other ideas?
I assume the "queen who stored a lot of cake" is Marie Antoinette, and so likely we're looking for something named after her. i.e. antoinette street or some such thing...but probably something less specific. i.e. in the right area maybe a maryborough, or some such would get us close enough (although it doesn't appear to be the maryborough golf course in Australia).