Subtle is the standard spelling of the adjective meaning (1) so slight as to be difficult to detect, (2) difficult to understand, (3) able to make fine distinctions, and (4) characterized by skill or ingenuity. Subtil is an archaic spelling of subtle. It is no longer used in any variety of English (though it is a modern word in French and German).
Subtle‘s corresponding noun is subtlety, though subtleness appears occasionally. Its adverb is subtly.
Examples
Subtle is the preferred spelling throughout the English-speaking world—for example:
The shift to the Earth’s tilt will have profound, if subtle effects on the length of the day and the passage of the seasons. [Daily Mail]
In a subtle nuance of language to indicate the slim hopes of finding any survivors, firefighters used the Japanese word for “search” instead of the more commonly used “rescue.” [Wall Street Journal]
In some neighbourhoods you might see an eye painted on a wall, a subtle message that locals are watching out for signs of disorder. [Herald Sun]
In the context of euthanasia, the “shortcut” subtext may be more subtle and difficult to discern. [Times of India]

