The correct order of the events is:
1. France colonizes Indochina;
2. France fights communist forces in Indochina;
3. France and the United States support an unpopular government in South Vietnam;
4. Vietnamese communists declare independence.;
5. France recognizes an independent North Vietnam;
France managed to colonize Vietnam, as well as other parts of Indochina in a very well planned, and gradual, systematic taking over. After some time, the nations in Indochina, including Vietnam, started to rebel against the French, thus multiple battles occurred. The forces fighting for liberation of Vietnam were mostly with a communist ideology. The French, as well as the USA, were supporting an unpopular traditional leader of Vietnam, which didn't really helped their cause, apart from managing to extend their influence in part of Vietnam a bit longer. The communist where victorious though, and they managed to gain full control of North Vietnam. The French had no other option than recognizing North Vietnam, and avoid further troubles.