A calque is an expression that is a literal translation of a foreign expression - a loan translation. Colm O Baoill, professor of Celtic at Aberdeen University, in the course of an essay in the superb Edinburgh History of the Scots Language (edited by Charles Jones, published by EUP at a price I, for one, can't afford - £140 sterling), teases out the phrase "to let on", to pretend, but in a negative construction "divulge" or "admit" (as in "Never let on . . . " in both Scots and English). In 12th-century Irish, and in the other two modern Gaelic languages, we find expressions of which "let on", meaning "pretend", is probably a calque.
The form of the preposition used for "on" in Middle Irish is the personal one (form, "on me", fair, "on him", etc.). Thus, leicid fair would mean "he lets on him"; now consider that Scots had the modern-sounding "he is not so daft as lets on him" in 1589. But the problem with saying with absolute certainty that "let on" reached Scots from Gaelic is a gap in the written evidence between the 12th century and 1589. The earliest instance of the negative use (which is not found in early Gaelic) dates from 1629: "Christ letteth not on him that hee either heareth or seeth me."
The Oxford Dictionary says of both usages that they are "original dialect and US English": it found that the earliest non-Scottish instances of "let on" are 1828 for the positive and 1848 for the negative usages, both from America's east coast. If I were Mr Paddy Power I would offer you very short odds indeed that the expression "let on' `reached English from Scots through medieval Irish; but modern Irish, operating through American English, may also be a claimant.
And how about the use of "and" in constructions such as these which I myself have heard: "You shouldn't be lifting things and you pregnant" (Ireland); "he drove the car and he drunk" (Galloway). "You were so good to come to see me and you so tired after your journey" (Lancashire). This use of agus "and" is found in all three Gaelic languages and in medieval Welsh too. It has been in Irish, Baoill reminds us in his masterly essay, since the 8th century.
The French calque means a tracing. You'll hear them by the score if you give a while in any part of rural Ireland. Our rich English is liberally garnished with them.