Final answer:
France controlled Indochina during the era of New Imperialism until they were ousted following their defeat at the battle of Dien Bien Phu in 1954.
Step-by-step explanation:
The country that had control of Indochina during the period of New Imperialism was France. Starting from 1858, France began its dominance in the region, which includes present-day Vietnam, Laos, and Cambodia. France's involvement deepened over time; by 1887, it had established protectorates over the entire region of Vietnam and over Cambodia.
Laos also became part of French Indochina following military conflicts with Siam (now Thailand). This control was interrupted when Japan seized the region during World War II, but the French aimed to regain control after the defeat of Japan in 1945. However, they faced significant resistance and were ultimately defeated in 1954 at the battle of Dien Bien Phu, signaling an end to French colonial rule in the area.