Why did President Eisenhower believe it was important for the United States to support the French in Vietnam?
He wanted to establish bases in Asia that would be close to China, Japan, and the Soviet Union.
He believed it was the duty of the United States to assist all nations in need.
He expected that in return for the aid, France would become a stronger trading partner.
He thought that if one Southeast Asian nation fell to communism, more would follow.

The domino theory was prominent in the world's politics between 1950 and 1980. It stated that if one nation came under the influence of communism, then the surrounding countries would follow like in a domino effect.

After the Soviet Union ruled over most countries in Eastern Europe, Eisenhower was aware of the threat of communism spread. After the Korean War he was scared that the Communists would take over Indochina, as Korea was close to Vietnam. Burma, Thailand, Malaysia and Indonesia all had popular Communists movements active there at that time as well. The domino effect was very likely to happen in Southeast Asia, so he supported the French in Vietnam.