Yes, most of the early settlers to New France were men. The few women who came had to pay their own passage, not necessarily an easy task for single women in the 1600s, even if they were inclined to the hardships. In the mid part of the 17th century, concerns were raised that the colony was not viable due to population size and lack of growth. A letter from Jean Talon (at the time, the Intendant of New France) stated, "send us strong, intelligent and beautiful girls of robust health, habituated to farm work."

Les Filles du Roi, or the King's Daughters, were more than 800 women sent from France to the colony of Quebec over a period of 10 years from 1663 to 1673, specifically to marry settlers and army personnel. Most were common women, from farming families in the northern parts of France. They were called the King's Daughters because their doweries were provided by the Crown. Records show 852 women, who apparently volunteered - though I can't find any proof of that, someone else here might have more. The sources I've found state that more children (or more children living to adulthood) were born to the French women rather than the Native women who had married settlers. In 1671, records show nearly 700 births from Filles du Roi marriages. Families with more than 10 children got an extra annual pension from the crown - about $6000 in today's money, a pretty good incentive. Approximately two-thirds of French Canadians can trace back to a Fille du Roi in their ancestry.

The first line in Thomas Laforest's "The King's Daughters", is perhaps a more succinct answer to your question: "Rare indeed is the French-Canadian who does not have a Fille du Roi, or Daughter of the King in his ancestry."

Sources:

Les Filles du Roi, Juliana L’Heureux (1998)

The King's Daughters, Thomas J. Laforest (1989)

Most French Canadians are descended from these 800 women, CBC Canada, The Story of Us (2017)

I might be late but it's a good question.

Most of the sources cited in the other answer are not from historians. If the impact of the Filles du Roi had without doubt an important factor, it does not tell the reason why most people in Québec have an insignifiant Native ancestry. I will base my answer on what I learned in my classes on this subject at the University of Montréal.

At first the goal of the french colony in North America was more economically oriented and with a very scarce population of trappers and merchants. It was under the control of a compagnie: Compagnie des Cent-Associés de la Nouvelle-France. This changed with the time, most notably when the king took direct control of the colony in 1663. The original document

With this change of control came more emphasis on the population and occupation of the vast territory notably with a direct help from the king with the Fille du Roy. As /u/It-Was-Blood noted this had a big impact on the population at the time. Most importantly, the common french migrants were not immigrating permanently. On 30 000 migrants from France only 12 000 remained in the New World. The other were mainly ''engagées'' who were payed to work for a certain time in the colony.

Under the French regime the colony and population were closer to the natives. They were allies in wars and trade partners. For exemple, Montreal remained an important trade hub in the fur trade up until the XIXe century. Still, in the mind of the French, relation with the ''indiens'' where centered on a logic of submission. ([Notably religious submission] (https://www.utpjournals.press/doi/abs/10.3138/jcs.18.3.5?journalCode=jcs)) However, ''métissage'' was not common as this was more a meeting of two distincts societies than a melting pot. At the time of the war of Conquest (the 7 years war) there was a real concern from french officers serving in New France about the ''ensauvagement'' of the local population. The fear of a ''barbarisation'' was more based on observations of some differences between ''Canadiens'' and french peasants more than a real métissage. This was mostly a result of the assimilation of traditional natives activities like smoking pipes, snowshoes and hunting. This assimilation remained shallow, mainly centered on practical techniques like the ones listed above.

I would argue that the biggest rift between the ''canadiens'' and the Native population was the English regime after 1763. In the pre-French Revolution world, it was common in Europe to have a king of a foreign culture ruling over a groupe of people not related in culture. For exemple, most of the king and queens of Europe in the XVIIIe century were speaking french. In this context, the Canadian population, catholic and french speaking, needed to assert its European roots to gain recognition by the British gouvernement and, at that time, it was through the affirmation of a white European identity.

Writer or religious mens like François-Xavier Garneau and L'abbé Ferland theorized most of the stereotypes regarding the natives. Such accusations as, that they are lazy, alcoholic, that they have no culture or history. Such bashing created a definitive cultural barriers only reinforced by more administrative segregation and discrimination. Such racism was not only the ''canadiens'' but also of the anglos. In this aspect, this racism was more a common theme than a distinction. The historian Mathieu Chaurette really bring light to this subject in is texte ''L’opposition des missionnaires catholiques à la scolarisation des Autochtones au Bas-Canada, 1826-1845''

TL DR Québec have a nearly insignificant native ancestry because both societies did not mixed under the french regime and its affirmation of a European identity was seen as a way to gain legitimacy in the British administration

note 1: as you can probably tell i'm not a native english-speaker, please excuse any errors. note 2: If you want to go deeper there is a text by the historian Allan Greer which places the rebellion of the patriots in a context of liberal revolts inspired by European ideas. You can really see how the Canadian society is link more with Europe and the United states. It is: La république des hommes : les Patriotes de 1837 face aux femmes

A good book to read is "many tender ties" by sylvia van kirk

She chronicles the opening of the west and the intermarriage of the trappers to native families. At first it was for access to the furs for trading. Then it was looked down on. Excellently written and easy to read. Even for a dummy like me.

Quebec trained history teacher. I am going largely on my memory here but I could probably dig up some old textbooks if I need to, though I will say this is an area that's neglected in the high school curriculum that I was taught to teach.

One reason might be the extreme uh, fertility let's say, of French Canadian families, which I'll address in a few places below. The other would be shifts in the relationship between white settlers and Quebec's First Nations peoples over time.

Let's split this into a few eras, starting with New France.

The colonial authorities implemented multiple means of encouraging population growth beyond just the involvement of the filles du roi. Bonuses were paid to those married by a certain age and fines levied against the parents of unmarried children past a certain age. Bonuses were paid to families with large numbers of children. The Catholic Church encouraged marriage and procreation, valuing large families and fertile women and discouraging people from not marrying or marrying too late. The church, after a time, was also not big on the coureurs des bois marrying first nations women because it encouraged the coureurs des bois to "go native" as it were.

During the British colonial era, immigration from France was largely cut off, but the Quebec population was sizable enough by then to be a concern to British authorities. In order to appease the population, certain concessions were made to maintain the primacy of the Catholic Church in Quebec society. And the Catholic church continued to be, well, Catholic. In this era, the stereotype of Catholics=babies was pretty accurate.

Immigration was largely white, and considerable numbers of Irish Catholics immigrated in the 1800s and intermarriage and adoption of Irish orphans was common, such that many French Canadians have some Irish ancestry, including the adoption or passing down of very Irish first and last names, and you will find francophones named William living in the Gaspesie.

At this time, intermarriage between French Canadians and First Nations would have been socially frowned upon; one good example of this is famous Metis leader Louis Riel. During his youth Riel spent some time in Montreal and courted a young French Canadian woman, but her family ultimately rejected him as a suitor due to his heritage. (I realize Louis Riel is primarily a figure of the Canadian period but as this was an event from his early life it happened before confederation.)

Canada: I don't know as much about social attitudes toward first Nations intermarriage in the Canadian period, but I can tell you that up until the 1950s the Catholic Church held sway over Quebecois society in a very strong way. They continued to encourage large families, conservative values, and discouraged intermarriage between non-Catholics and Catholics. In that sense, it meant Catholic French Canadians usually married Catholic French Canadians, and had many children. They might intermarry commonly with other Catholic Europeans to an extent.

In the Canadian period, FN status and intermarriage would have been governed under the Indian Act. The Indian Act was written so that women who married non-status men lost their status and were thus unable to continue to be part of their communities (they couldn't live on reserves, couldn't pass status to their children, etc.) This would have made women think twice about marrying outside the band, and would have obscured the descendants of the marriages that did occur from knowing about their FN ancestry or being involved in the FN community.

General comments: There is talk in Canadian history as well about the idea of the "revenge of the cradle;" that until the 1950s, high birth rates were encouraged among French Canadians as a matter of national pride and ensuring their cultural survival and place in Canadian and North American society. I'm wary of this as an explanation because I can't find sources on it from the time, even though it is a popular explanation. It seems more likely to me that rather than being an intentional thing, this was a side effect of Quebecois culture that was later seized upon by nationalists. If anyone wants to expand on this idea, go ahead.

Over time, some other factors may also have served to reduce the number of opportunities for interaction between whites and First Nations. These include the devastation of FN communities by disease; the displacement of FN communities from the St Lawrence River Valley, where the majority of French Canadians lived, to further and further marginal lands; and the eventual placement of FN peoples on reserves, many of which are far away from lands where the majority of whites lived.

In short, intermarriage was a relatively early phenomenon that was only common in the period of New France. While most Quebecois probably have one or two first Nations people in their family tree, they are not really that mixed in that respect. The habit of French Canadian families of producing many many children has probably served to dilute the impact of those early marriages on the later Quebec population.

I hope this is a detailed and accurate enough answer for this sub.

My grandfather was born in Quebec, and his family was all French Canadian. How could I go about finding if any of my ancestors were the King’s Daughters? Thanks!