Is it common to use the borrowed noun-adjective form for borrowed French phrases?

The point about these phrases is not whether they came from French (which I find dubious), but that they are unique titles. There are dozens of general attorneys, but only one Attorney General. Similarly with Secretary-General (of the UN) as opposed to General Secretary of a union or organization, and Surgeon General in the US. Court martial is harder to see, but it may be an obsolete conceit that all sitting military courts are part of one Court Martial (as Henry said), in the same way that the Supreme Court may consist of any number of judges, and may even hear two cases at once, while remaining formally one Court. ("Court Supreme" sounds like a dessert, and lawyers hate being made fun of.) I don't know about Notary Public, but it doesn't seem unlikely that (for example) only one lawyer in each town was originally allowed to use the title.

The titles you list are just that: titles of offices held by certain notables. A public notary, while the term may be understood, would not be official and may not even be legally accurate.

Although reversing (or unreversing, however you will have it) the order may appeal to your sense of propriety, a "general attorney" is simply not the same thing as the Attorney General.