The country that colonized Vietnam (and other parts of Southeast Asia) during the 1800s was France. It took more and more control over the area as the century went along.
By the 1800s, France had had a presence in Vietnam for some time. French merchants and missionaries had been active in that country. But then the Vietnamese started to worry that the French were having too much influence over their country. That made them start to resist French influence. The French became concerned about this and therefore used military means to force the Vietnamese to accept French influence. The Vietnamese signed a treaty with the French in 1862. From that point on, the French took more and more power. By the end of the century, they were in complete control of what came to be called French Indochina. This was the area that is now Vietnam, Cambodia, and Laos.