It is safe to say that our world wouldn't be nearly the same today, due to the events crammed into the short period of 1580 to 1763, more so than all other eras in history combined. Many races and religions were expanding and looking for new and better ways to live, and a lot of them had the same idea, that the only way they could do that was in the New World. The imperial goals of England, France, and Spain all differed somewhat, but in the end, had the same meaning: to conquer the land that was North America.
The English seperatists were the first people to officially settle in America, therefore not having much competition for anything as far as land, resources, or power. England's main imperial goal was to spread English culture throughout the New World. As a broken-off group of their old country, especially, they needed land to expand their community and bring more dominance to their ideas, which is why North America, thousands and thousands of square miles of nearly uninhabited land, was the perfect place to do it. Because they were the first country to settle down, they initially had no other imperial goals.
The French, on the other hand, had much to accomplish, being as they originally had little to no power in Europe, as well as not much respect. Their main imperial goal was to spread catholicism. You could compare this to the English's goal of spreading their culture, because catholicism was a very large factor of France's culture, and it differed very much from the vast majority of England's religions, which were Protestant. Now, with competition of many other countries in the New World's melting pot of races, France had something else they wanted to gain: resources. In their country, the beaver was basically their only item of value to other traders. But North America brought prosperity to whoever could get it first,...