Well, Sara, at least you remembered some of it--but your response illustrates that old saw that a little knowledge is a dangerous thing. It is true that the felt made from the undercoat of beavers was used to make hats--but they weren't made in North America, they were made in Europe.
Kings paid for cheap expeditions, exploration expeditions. So people like John Cabot and Jacques Cartier would get a ship and go exploring. But colonizing is a different thing altogether, and a damned expensive business, so that worked a different way. The people who wanted a colony would go to the king and get a charter. In England, in the reign of Queen Elizabeth, the coast of North America was called Virginia (the scam was that Elizabeth was the Virgin Queen), and a charter was issued for the Virginia Company, which didn't get around to a succesful colony until Elizabeth was dead. The first colony, at Roanoke Island, was established in 1584, but the colonists disappeared and the colony was a failure. There's an intersting story behind that, but it's not pertinent here.
Elizabeth died in 1603, and her cousin, King James VI of Scotland became King James I of England (you know, the King James bible?). The Virginia Companies were chartered by James in 1606--one was the Virginia Company of London, and they estalished Jamestown in1607. They eventually went bankrupt and were taken over by the royal government--ironically, just before they started to get rich from tobacco. The other was the Virginia Company of Plymouth. It was a failure, too, but its options were bought up by some Puritans who got a charter for the Massachusetts Bay Company. Usually charters said that the Governor and Selectmen (roughly, the board of directors) would meet in London, but the Purians were slick, and their charter didn't say where they would meet. So, in 1630, after James had died and his son Charles was King, the Massachusetts Bay Company elected John Winthrop as Governor, and he, the Lieutenant Governor and the Selectmen took the charter itself, and sailed to Massachusetts. They weren't actually trying to make profit, they just wanted to establish a "godly republic" in the wilderness--"shining city on the hill" and all that. Later on, after three civil wars in England, the execution of King Charles I, and a good deal of other turbulent water under the bridge, the charter of the Massachusetts Bay Company was revoked and they became a royal colony. Gold wasn't in it, and neither were beaver.
The real doozie was the Company of Gentlemen Adventurers Trading into Hudson's Bay--the Hudson's Bay Company, chartered in May, 1670 by King Charles II, and still in business today, although on a much more modest scale. Those jokers got rich, really rich, from the humble beaver. Charles II owed money all over the place, and most of the charters handed out were to pay his debts. For example, he and his brother owed a very large sum of money to Admiral Penn, and after he died, they paid that off by giving his son, William Penn, the colony which became Pennsylvania. They gave about half of Virginia to Lord Fairfax, and they paid off a lot of lesser debts with charters and land grants in the two Carolina colonies (Charles, Carolina, get it?). So nobody expected the king to get rich off those colonies. The only colony which brought in wealth from beaver pelts was New York, which Charles' brother James (Duke of York, get it?) stole from the Duch. Indians would trade their beaver pelts at Albany. The Hudson's Bay Company was making money hand over fist, and they didn't want any colonists.
That's because the colonists didn't trap the beaver, the Indians did. They brought in beaver pelts and furs and traded them for European goods. That's why the HBC didn't want any colonists. They didn't want anybody ******* with the Indians, who were their collective cash cow.
With the French, things worked somewhat differently. Samuel de Champlain was part of exploratory expeditions to what is now Canada in the early 1600s, and he eventually establish the city of Québec in 1608. He was, effectively, the governor of New France, but he was not a member of the nobility, so he was never given the actual title of governor. With the French, colonies were under the control of the ministre de marine
--the guy we would call the Secretary of the Navy. He made a decent living through acceptable graft. If you wanted a job in New France, you paid him a visit, and you took some gold along with you. Governors were often appointed by the king, who would be paying off debts or rewarding people for services rendered, such as in the case of Frontenac, who was twice governor of New France. But the kings of France didn't make any money out of Canada, because theft in office was an institution there. From the poorest raggedy-assed nobleman, down on his luck in Michillimackinac to the governor and intendant, everyone along the line was stealing from the fur trade hand over fist. Just as the Dutch and English did, the French would wait for the Indians to show up with the beaver pelts and furs, and then trade them for French manufactured goods. The Indians actually preferred the French goods, which were much better than the cheap **** the English were handing out, and they much preferred the French brandy to the rot-gut rum the English handed out.
So, in the beginning, the Hudson's Bay Company was making money as thought here were no tomorrow and the French were getting rich. But the French officers and officials stole from the king at every step along the way, and Canada was, on the whole, a losing proposition for the crown. That's why they gave it up so easily in 1760. Voltaire, when he was told that Canada was handed over to the English simply commented: "So many acres of snow." What a fool. The English colonies, of course, didn't prove to be any cash cow for the kings of England either, and their attempts to profit from the colonists would eventually lead to some unpleasantness, the result of which was the foundation of the United States.
I suspect what we have here is a kid who wasn't paying attention in class and now wants somebody to do his homework. From the sound of things, either his teacher or his textbook is peddling some pretty simple-minded bullshit, which is why i didn't give a serious answer to begin with.