Yes, the vast majority of French Canadians, including the 6 millions in Quebec, are descended from those original settlers. As to how, the answer is simple, but is worth exploring further, given the almost legendary status of French Canadian natality.

For the 1st century after the conquest, natality in lower Canada (Quebec) was high, but not unusually so, given that it was a colonial, rural, catholic population (all factors that tend to raise birth rates). From 1763 to 1870, Quebec grew quickly (to roughly 1.2 M people) but birth rates in Quebec were not outpacing those in neighbouring Protestant Ontario. Still the province's population was growing faster than its economy; from 1830 on, almost a million French Canadians relocated to the US, to work in New England factories. About half of those settled permanently, giving birth to a big Franco-American population in the Northeast that got gradually assimilated during the 20th century.

The late 19th century is when French Canadian natality started standing out. Not because Quebec women were having more children, but rather because women elsewhere were having less. In Europe and the US, rapid industrialisation and urbanization lead to deep societal changes characterized, among other things, by a much lower birth rate. In Quebec during that period, those effects were felt to a much lesser degree.

As for why that is, there's no one universally accepted cause, but the power of the Catholic clergy in Quebec society during that time is likely part of the answer. The Church wasn't only tending to the religious needs of the population, but also controlled education and healthcare in the province, and had major political and economic influence. During its ascendancy, the Church preferred to orient its flock toward the simpler rural life, encouraged high natality and discouraged contraception.

But by the 1940, the Quebec birth rate was finally starting to fall. After two world wars, a new wave of industrialisation and urbanization, and with increased questioning within Quebec society of the sociocultural control of the Church, Quebec was changing. By the 60s, Quebec was going through its Révolution Tranquille (Quiet Revolution) which saw a massive embrace of progressive, secular values along with the rise of Quebec nationalism. While this was happening, the demographic decline Quebec had avoided in the preceding century rapidly took place: Quebec went from having the highest birth rate in Canada in 1959 to the lowest in 1971, and it has stayed relatively low ever since. In turn this has given rise to a complex debate centered around immigration and identity that continues to this day.

Anecdotally, I can see those demographics trends in my own family. My grandparents (all French-Canadian, though from different socioeconomic backgrounds) all had from 8 to 15 siblings. My parents (born in the late 50s) each had 2. My dad has more than 40 cousins; I have none.

I'll add that this phenomenon of high French Canadian natality is often called "La revanche des berceaux" (revenge of the cradles), a term popularized by Jesuit Louis Lalande in 1918. It's often used in a narrative where it was born out of the collective will of French Canadians to ensure "la survivance", using fertility to counter English attempts at assimilation, with the support of the Church. It makes for a nice story, but AFAIK, there's zero evidence to support this kind of voluntary, deliberate manipulation of demographics. Frankly, it's a bit far-fetched.