I'm oversimplifying, but it ultimately comes down to the economic aims of the British Colonies vs. New France.

With some exceptions in the earliest generation (Roanoke and early Jamestown), the British colonists intend to settle in North America. For them, the land, and the raw materials that can be derived from the land, are most important.

Conversely, the French decide on trade as their focus in North American almost immediately. As the article on New France from The Canadian Encyclopedia indicates, France's expansion into Canada is there primarily to facilitate the fur trade. As a result, a lot of New France ends up being populated by young men looking to make their fortunes in the fur trade and who then return to France. You see a similar mentality with the British in Barbados and South Carolina, but more often than not the sons of Carribbean planters end up settling and focusing on long-term profit.

Outside of Canada, you see the pattern repeating for the French as well. In The Southern Frontier (which is, alarmingly, still one of the best works on native, French, Spanish, and English relations in the colonial Southeast), the French focus on commanding riverways rather than building large land settlements. By controlling the rivers, they're more able to facilitate trade with native peoples and are less occupied with building large, permanent settlements.

Without a focus on settler colonialism, New France doesn't get the influx of people you see in British North America. Wind the clock from the earliest settlements to the Seven Years' War with these two paths in mind, and you end up with a massive population discrepancy between the two groups.

The Seven Years' War (1756 - 1763) was actually the name to the global conflict that followed the beginning of the French and Indian War (1754 - 1763) that actually started in North America two years prior. The name change was primarily attributed from Europeans seeing the initial conflict as solely a North American affair, where a by 1756, there was fighting across the globe. While the French and Indian War primarily was fought between Native Americans, France, and Britain, the Seven Years war was fought by many countries, including Hanover, Prussia, and Portugal (although they fought only in the final two years) and Spain and the Holy Roman Empire (among others).

The war itself was vastly complex, fighting across Europe but also in the Caribbean, Philippines, Africa, and India in addition to the fighting in North America. So to answer your question, "why did it last so long," it's because the war was a global war, spanning many countries and many locations, which greatly complicated the prolonged the conflict.

Your primary question presupposes that the people who inhabited North America were the primary people fighting in the war. This is in fact, untrue. For France, the people who lived in New France primarily were connected to the French fur trade. Unlike in British North America where people were immigrating there for a variety of reasons (among them being religious and economic equilibrium that could not be achieved in England) and setting up new families, this was not the case in New France. As the Smithsonian Institute explains:

French traders established settlements at Québec and Montreal along the St. Lawrence River in the early 1600s. French Jesuits also traveled to the colony to bring Catholicism to Native peoples. But New France focused primarily on the fur trade. Relatively few immigrants left France to settle in the New World, and some who did were Protestant Huguenots, welcome in British colonies but not in Catholic New France. Despite limited immigration of Europeans, New France laid claim to broad swaths of the continent, based on extensive military and economic alliances with Native peoples.

New France became a treasure trove of wealth for the people of France, and they didn't see a need to inhabit the land in the same ways that Britain did with their North American colonies.

Their population was larger than you initially said, (70,000 is the typical number I've seen cited), it was too small to field proper militias. So the French military did occupy their forts and borders using actual french soldiers, unlike British North America which used a combination of militia as well as British regulars. So for the French side, the lack of their actual population in North America didn't immediately affect their standing in the war since they were fielding units of soldiers from their homeland.

Cold weather also had no measurable influence on the population differences. Judging from this map, the territories of New France stretched from Louisiana up to Canada and had considerably more land than that of Great Britain. Also, Massachusetts and Main, which both border the Canada territories and experience almost as harsh of winters as those above them, had a combined population of 269,000 people by the 1760s, almost four times the entire population of New France. So as you can see from that data, location and cold weather had no bearing on New France's population.

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Edited: to expand on several points

The other two comments are great, but they don't really go into *why* the fur trade was so different in terms of economic activity. I shall try and answer just that bit.

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So, the fur trade is a bit different from any other colonial economic activity. Unlike farming, it was reliant on a relatively finite number of animals, an increase in the trade requiring the discovering of new native peoples, with their own spheres of influence and therefore access to pelt bearing beaver. Due to this, supply could be very hard some years and very high others, meaning the number of people need for each harvest was much lower than, say, farming. The people doing most of the work were native Canadian and American nations, meaning you just didn't need a lot of French people (and hence why losing Newfoundland and her fisheries to the British was such a blow to French colonization)

Secondly, fur is a very odd commodity. You can eat foodstuffs, everyone can wear cotton clothing, iron is useful for many things, but beaver fur? That gets its value from style.

So you have a problem. Beaver fur hats cannot be too expensive, because the upper class other than the most noble of dukes to buy them. But! You don't want them to get too cheap either, because the entire reason the hats are valuable is because they're cool and fashionable, and if the poors start wearing them they'll lose the social value that makes them valuable.

You see the issues there yeah? Because everything has to be just right. You have to take enough but not too many pelts to not flood or starve the market, you have to constantly be scouting for new native american nations to supply you with pelts later, and you have to pray that beaver hats remain cool in continental fashion, because if they aren't then the entire system becomes unprofitable in the way its practiced.

Given this level of risk, and the high amount of capital that needs to be invested, why would you bring more people in? It just means profit margins get even riskier, and farming the land means you remove beaver habitat. The level of risk means that monopolies form more readily, and these monopolies' interests are threatened by large scale colonization.