England: The British sought to Christianize the Native Americans, but weren't so diligent at it. They tended not to marry Natives. Their relationship depended on the trade of furs and guns with them, so when supplies ran low, the relationship between the two people hit a real low.
Spain: Queen Isabella ordered the fair treatment of Natives and believed they should be treated equally to her other citizens. However, most explorers did not follow her orders and enslaved and brutalized the Natives, just like the British. However, after a period of Christianizing the Native Americans, they began to intermarry and produce offspring of multiple races.
France: The French recognized the harmful results of diseases spread by earlier Europeans, and made attempts to alleviate the deaths occurring. They also tried to have peaceful relationships with the Native Americans and also intermarried. This isn't to say that all relationships were peaceful between the French and the Natives, but it is the general mindset of the time.