Weird that Russians wouldn't use a native root for such a basic concept. Plenty of Slavic languages have variations on "tajna." Maybe it's some bureaucratic term using a Westernized root to be fashionable.
Of course Russian has the word «тайна». It's the generic term for hidden, classified, protected, secret, or unknown information. And «государственная тайна» would be "state secret".
But the stamp on the maps wasn't just for indicating that they are some sort of state secret. It was for indicating the exact level of secrecy in the Russian classification system.
Those levels are «особой важности» (literally: of special importance), «совершенно секретно» (lit.: completely secret) and «секретно» (lit.: secret). And in US government terminology, they approximately correspond to "top secret", "secret", and "confidential", although the boundaries between the levels are defined somewhat differently.
In Russian Empire the imperial court mostly spoke French so lower classes, aspiring to sound more like nobles, borrowed a whole lot of French words. Because of this many Slavic words now sound archaic or pretensions to a Russian speaker. E.g. тайна in Russian is more like 'enigma', definitely not 'classified/secret'.
Thanks for this comment, this is exactly what I was wondering. It's similar to how Croatian adopted mostly English words for computer hardware, and the attempt by the government to push Slavic-rooted replacements ended up sounding silly.
It's an established idiom, same as военная тайна or, even better, тайный советник. Words that make up an idiom do not carry the same meaning outside one and vice versa.
