How did the French and eventually the British manage to take control of the entire continent of North America?

The French and British were always quite powerful, and have been in conflict with each other for a long time, but one thing they have in common is that they managed to take control of North America.

Some of the ways they managed to this were quite similar. They both had more advanced weapons than the Native people of North America, they both had great armies, and they both brought sickness from their own country to North America.
Even without giant armies, the French and British would have probably been able to take over most of North America as some Native Nations were quite peaceful, and their weapons were made of flint, bone and metal. These weapons would not last very long against guns and other weapons made out of steel. With the grand armies, both France and Great Britain could keep their colonies and the Natives under control. Many times the soldiers would also be the police of a colony. As for the Natives, some of they had very few people and/or resources after European contact so they had no choice but to give in to the French or British whims. One of the biggest reasons that the population of several Native Nations were decimated was that the french and british brought over sickness from their countries, sickness that the Natives had no defence against. some of the sicknesses were smallpox, influenza, bubonic plague, and pneumonic plagues.
With weapons, armies, and sicknesses of the french and british, there is no wonder how they were able to take control over North America. Seeing as they also had a rivalry, France and Great Britain competed to see who was the most powerful. Unfortunate as it was for the environment and for the Native Americans, the french and british take over of North America was an essential step on our journey to today.
Souces:
en.Wikipedia.com (2013). Population history of indigenous peoples of the Americas. Retrieved from http://en.wikipedia.org/wiki/Population_history_of_indigenous_peoples_of_the_Americas
Simkin J. (2013) Indian Weapons. Retrieved from http://www.spartacus.schoolnet.co.uk/WWindianweapons.htm
Dr.Olson-Raymer G. (2013). Evolution or Revolution? Retrieved from http://users.humboldt.edu/ogayle/hist110/unit2/revolution.html