The First Indochina War affected the world by the fact that it led to the creation of the independent countries of North and South Vietnam. This creation then led to the Vietnam War that involved the United States.
After the end of the First Indochina War, Vietnam was split into two parts. North Vietnam was communist controlled while the South was controlled by a government friendly to the United States. This made Vietnam an important part of the Cold War. North Vietnam and its supporters in South Vietnam started to try to subvert South Vietnam and make it have a communist system. This led to American involvement in what we now call the Vietnam War.