My favorite Yankee, H. L. Mencken, provides origins of many terms in the American vernacular. You will recall Mencken's unpopular view of Lincoln's 'Gettysburg Address'. Before giving his explanation and analysis, here are lines from the 1992 film version of Last of the Mohicans, based on the French and Indian War. Four times in this scene Nathaniel uses the Indian version of the French word for English --

For the first time, Nathaniel turned and spoke directly to Magua. "Would Magua use the ways of le Francais and the Yengheese? Would you?"

"Yes!" Magua spat back at him.

Turning back toward Sachem, Nathaniel said, "Would the Huron make his Algonquin brothers foolish with brandy and steal his land to sell them for gold to the white man? Would Huron have greed for more land than a man could use? Would Huron fool Seneca into taking all the furs of all the animals of the forest for beads and strong whiskey? Would the Huron kill every man, woman, and child of their enemy? Those are the ways of the Yengheese and the Francais traders and their masters in Europe infected with the sickness of greed."

Pausing, Nathaniel glared at Magua, allowing Duncan to finish translating his words before continuing. "Magua's heart is twisted. He would make himself into what twisted him. I am Nathaniel of the Yengheese, Hawkeye, adopted son of Chingachgook of the Mohican people. Let the children of the dead Colonel Munro and the Yengheese officer go free. This belt," Hawkeye said as he lifted the wampum belt, "which is a record of the days of my father's people, speaks for my truth."

To return to origins of the term "Yankee", here's what Mencken has to say.

Whether or not Yankee comes from an Indian dialect is still disputed. An early authority, John G. E. Heckwelder, argued that it was derived from an Indian mispronunciation of the word English. Certain later etymologists hold that it originated more probably in an Indian mishandling of the French word Anglais. Others derive it from the Scotch yankie, meaning a gigantic falsehood. Yet others derive it from the Dutch, and cite an alleged Dutch model for “Yankee Doodle,” beginning “Yanker didee doodle down.” Finally, Ernest Weekly, in his Etymological Dictionary, makes the conjecture that it may be derived from the Dutch Jan (=John), possibly by back-formation from Jan Kes (=John Cornelius). Of these theories that of Heckwelder is the most plausible. But here, as in other directions, the investigation of American etymology remains sadly incomplete. An elaborate dictionary of words derived from the Indian languages, compiled by the late W. R. Gerard, is in the possession of the Smithsonian Institution, but on account of a shortage of funds it remains in manuscript.

For the Dutch “Yanker didee doodle down” ditty, see the following --
http://www.recess.ufl.edu/transcripts/2004/0702.shtml

The fictional name 'Jan Kaas' may have been been an antecendent for 'Johnny Reb' and 'Billy Yank'.

For anyone interested in native American origins of words now in contemporary language, here's more by Mencken -
http://www.bartleby.com/185/8.html

BTW, aside from being something your wife will enjoy, "Last of the Mohicans" is a great black-powder movie. It's filmed in western North Carolina, the final scene being done on Chimney Rock in Hendersonville NC.