A high percentage of the people who went from France to North America in the 16th and 17th Century were in the fur trade, or Clergy. The male - female ratio of European immigrants was probably at least 50-1, and many of those females were nuns, or monogamous. One would expect most of the Catholic missionaries and supervisors to have had few descendants, and fewer or the ones who weren't heterosexually celibate would have had Native partners.
By the 18th Century, the beaver felt hat fad had largely declined, (the main purpose of those huge hats was to protect clothing from liquid and solid human waste thrown from second story windows into the street below). Louis XIV sent les filles du Roi in the 18th Century, but there wasn't much additional emigration to New France. France just wanted to increase the population of the colonists who were already there. Very few of the men would have had full European ancestry after several generations.