In 1522, an Italian explorer named Giovanni da Verrazzano asked the French king for permission to look for a westward route to China. He and his fellow travelers ended up in North America.
These settlers found the going tough, since the weather in America was biting cold. The winters in America were much colder than those in France. They also had to fight diseases in order to survive there.
The French were interested in trading with the indigenous people of America. They would give the natives firearms and brandy, in exchange for beaver fur. However, French Jesuits were against giving brandy to the natives, because they wanted to convert the natives to Christianity.
The Jesuits claimed that the natives would be difficult to convert if they were drunk. The fur traders counter-argued that if they didn't give brandy to the natives, the English would give them rum.
The French always tried to maintain good relations with the natives. They would not settle on hunting grounds where natives hunted for game, they tried to learn their customs, and even married amongst them, to improve their relations. However, when the Jesuits tried to convert the natives to Christianity, the natives turned against them.
With the help of natives such as the Algonquin and the Huron people, the French fought the English and their allies―the Iroquoian people. They also had a problem with the coureurs des bois, the fur traders that didn't take permission to trade from their king.
Things really took a bad turn when two French explorers, Pierre-Esprit Radisson and Medard des Groseilliers, helped the English control fur trade in the region. The French took some territories from the English, but also ceded control of some. After these battles, France signed a peace accord with the English, called the Treaty of Utrecht.
The treaty specified that France would give up control of the Louisiana territory to its ally Spain. The Treaty of Utrecht was followed by the French and Indian War, in which France lost badly to the English.
Thereafter, the American revolution caused the English colonies to yield to the fledgling United States. Subsequently, Spain gave back control of the Louisiana territory to France, and the French emperor sold it to the United States in the famous Louisiana Purchase.
The French colonies were not successful, because their quasi-feudal system favored landlords over the common man. They also had a problem with the Huguenots at home. The Huguenots were Protestants who were not allowed to settle in New France. But when the king declared them illegal, they migrated en masse to New France.
The king also gave money to French people to emigrate to America, in order to increase the population of New France. The one advantage the French colonies had over the English colonies was that they stood united behind their army, unlike the English, who argued with each other on when to send their armies to war.
The effect of colonization of America by France, England, the Netherlands, and Spain cannot be overstated. The islands of Saint Pierre and Miquelon are still controlled by France to this day, and French is still spoken in the states of Louisiana, Maine, New Hampshire, and Vermont.
French is also the second most spoken language in Canada, where Francophones still carry on French culture and traditions.