The geopolitical impact of the colonization of the New World by old world powers such as France, England and Spain was dramatic and unprecedented, especially following the Seven Years War. While the war was fought mainly between France and England, all of the other powers of the time (Sweden, Prussia, Portugal, Spain, Austria and Russia) were also involved, whether through alliances with the main protagonists, or through direct conflict with them. It has been said that this was the first true world war, since it was so far reaching. Colonies in Asia, Africa, North and South America were gained or lost by the various powers, as a result of the battles fought in Europe and abroad.
While England's supremacy at sea was supported by regular soldiers in the New World, France's main focus was on the European theatre of war. Since the beginning of the colony, France had relied more heavily on local militias to defend New France than on regular soldiers. These troops were no match for the larger, professionally trained and equipped British regiments they faced. Traditional enemies, both countries fought ferociously and expanded enormous financial and human resources in the pursuit of victory and territorial expansion. In the end, both countries were left exhausted by the conflict, as were most of their respective European allies. Maintaining overseas colonies was expensive and difficult; fighting over them for years on end was disastrous.
As a result, the balance of power in Europe was altered dramatically, and some countries that had been considered great powers before the war simply never recovered. Spain never regained its previous status; neither did Portugal. France's naval forces were devastated, and would not recover for many years. Moreover, it lost most of its colonies in North America, except for St-Pierre et Miquelon (significant cod fishing grounds), la Martinique and la Guadeloupe (sugar) in the Caribbean.
Prussia, led by Frederick the Great, emerged as the new power in Europe. Its influence on the continent would reach well into the the tragic events of the first half of the 20th century.
There's really no end to the ways we could articulate the impact these regions had on each other in the post-Columbian period, but we can focus on a few.
- Agriculture was massively changed with the introduction of chocolate, corn, vanilla, tobacco, tomato, potato, and other foods, which diversified and strengthened European cooking and nutritional profiles as well as the economies of several countries. One estimate suggests that the potato alone spurred nearly a quarter of Europe's population growth.
- The markets were flooded with gold and silver, altering the trading system and leading to the kinds of diversified specializations by country that we see today (i.e. manufacturing vs agriculture and so on).
- The New World opened up new opportunities for colonization. This was famously addressed in the treaties of Tordesillas and Zaragoza, in which the world was divided exclusively between Spain and Portugal, although in practice the other European powers found this a laughably unenforceable mandate, and established colonies as they saw fit. Subsequently, shifts in European power significantly affected overseas holdings; for example, the Spanish were largely unable to leverage the economic power of their colonies, and when their power in Europe faded they found their colonies more of a hassle than a benefit.