Here is the version from Louis Allen, The End of the War in Asia. London: Hart-Davis, MacGibbon, 1976. Book One, "The Japanese Surrender in South-East Asia," Chapter 4, "French Indo-China," pp. 96-129, placed online in the Virtual Vietnam Archive of the Vietnam Project, at Texas Tech University.

De Gaulle planned on a 3 division corps for Indochina, but that was not to be - at least not at once (p.7 pdf):

But demobilization after the defeat of Germany so reduced the ranks of these divisions that they had to be combined. Besides, there seemed to be no way of transporting them to the Far East. French shipping was under the control of the Allied Shipping Pool and could not be released. The only unit actually present in Mountbatten's command was the 5th Colonial Infantry Regiment, itself only a battalion strong, under Colonel Huard. A Senegalese brigade was awaiting orders in Madagascar.
Unfortunately for French military plans, the natives were growing restless in Madgascar and their later 1947 Malagasy Uprising tied up many more French troops (primarily North African units) that otherwise could have been used in 1947-1948 Indochina.

That is getting well ahead of the story. The BLUF is that the US left Thailand and South Indochina to the British (Mountbatten) (p.18 pdf):

... headquarters was set up in Saigon under Major-General Douglas Gracey, GOC, 20th Indian Division. A brigade of this division had begun its fly-in on 15 September, and along with it Mountbatten established an Air Headquarters, with two RAF tactical squadrons, and a Naval Port Party.
Following Petri's Appendix I (p.455), 12 Sep 1945 saw the Saigon fly-in of the initial advance elements of the 20th Indian Div.; and also initial advance elements of the Huard Bn of the 5th Colonial Infantry Regiment (Troupes de Marine). The main body of the 5th RIC did not debark in Saigon until 3 Oct 1945 (Petri, p.455).

The latter weeks of September saw more chaos (p.21 pdf)

Meanwhile, events had gone much further than a mere proclamation. Gracey had permitted the French forces in Saigon to carry out their own coup d'etat. His troops took over the Saigon gaol and freed French paratroops who had been imprisoned by the Vietnamese. At Cedile's request, he allowed the men of the 11th Colonial Infantry Division, who had been under [Japanese] guard in their barracks since 9 March, to be rearmed and to leave the barracks. These French troops, about fifteen hundred of them, were spoiling for a fight, and went out into the streets to throw their weight about against the Annamite population. ... He [Gracey] ordered the 11th Colonial Infantry Division to return to their barracks and be disarmed. The Japanese command was given full responsibility for maintaining order.
The Japanese were indifferent to that task (pp.21, 22):

Order was the first casualty of the next phase in Saigon. The electricity generating station was attacked by Vietnamese on 24 September, and dozens of Frenchmen were kidnapped or killed in the port area. The next day, there was a massacre in the Tan Dinh suburb: three hundred French men, women, and children were abducted, of whom half were killed in atrocious circumstances. This happened in the space of two hours, while Japanese sentries stood by, idle and indifferent.

Colonel Peter Dewey of the OSS was driving to the Saigon airfield on 26 September when his jeep was attacked. He realized the Vietnamese had taken him for a Frenchman, and cried out 'Je suis Americain', but it was too late. His body was removed by the Vietnamese before Allied troops could rescue it.
...
It was in this atmosphere that France's two highest officials in Asia came on the scene. Leclerc landed in Saigon on 5 October, and the High Commissioner, Thierry d' Argenlieu, arrived on 30 October.
...
Leclerc had remained in Kandy until sufficient French forces were available for him to act effectively in Saigon. With the arrival of elements of the 2nd Armoured Division, and the presence in Saigon River of the chastened Richelieu, Leclerc began to take over from Gracey the responsibility for government and for disarming the Japanese. The 20th Indian Division packed its bags in January 1946, and on 1 March, with the approval of the combined chiefs of staff, IndoChina was withdrawn from South-East Asia Command.
The battleship Richelieu and its escort vessels had been operating under US command in the PTO.

Regards

Mike