From Patti (I typed "Petri" in the post above ), p.298, the 12 Sep 1945 fly-in was from Rangoon to Ton Son Nhut (Saigon) and involved Gurhkas, a Bn of the 15th Cav. Regt., 20th Indian Div.; and one company of the 5th RIC (Regiment d'Infanterie Colonial).

Patti devotes a chapter (Chap 32, "South of the 16th Parallel", pp.307-325) to the events of later September and early October 1945 in Saigon. One correction to Allen's book is that the barracks housing French prisoners was that of the 11th RIC (regiment, not a division), and that most of the prisoners were Legionaires and not Colonial Infantry (Patti p.316-317). The main body of the 5th RIC (roughly a 1000 men) arrived on 3 Oct 1945 on the French warship Triomphant (Patti, p.325). The Triomphant on 3 Oct 1945 was captained by Andre Jubelin.

The battleship Richelieu was under British fleet command in 1944-1945 (pre-VJ Day), and was not under US fleet command (as stated by Fall in his Two Viet Nams, p.67). From the Wiki:

After V-J Day, during the last four months of 1945, Richelieu took part in the return of French forces to Indochina, particuliarly at Nha Trang, with her Fusiliers Marins landing party, and delivering gun support. When Richelieu left for France, the crew received congratulations from General Leclerc, the French Commanding General in Indochina.
Besides the French warships Triomphant and Richelieu, the Dutch-British troop transports, Queen Emma and Princess Beatrix, hauled French troops into Saigon in October 1945.

Indian Ocean

Queen Emma was decommissioned to be adapted for service in tropical waters at Harland & Wolff at Belfast. The works were completed on 29 March 1945, and on 5 May Queen Emma sailed with Convoy KMF-44 for India, arriving at Bombay on the 26th. Queen Emma remained in India until the Japanese surrender in August. She then took part in Operation Jurist - the reoccupation of Penang by British Marines.[2]

She then embarked French troops, and escorted by the French battleship Richelieu, sailed to Saigon. On the return trip, Queen Emma was damaged by an acoustic mine. Her main engines were knocked out and the ship had to be towed. However, emergency repairs were made and she reached Singapore under her own power.[2]

After this Queen Emma transported Dutch women and children from Japanese concentration camps, and took British troops to Batavia, Semarang and Soerabaja.[2]
and:

Indian Ocean

Princess Beatrix operated for a time between the Clyde, Avonmouth and Liverpool before she was decommissioned to be adapted for service in tropical waters at D & W Henderson Ltd., Glasgow. She then sailed to the Indian Ocean, arriving at Trincomalee on 15 July 1945. A few days after the Japanese surrender she then took part in "Operation Jurist" - the reoccupation of Penang by British Marines.[2]

Princess Beatrix then acted as troop transport, sailing to Colombo, and taking French troops to Saigon. On 29 September [JMM: this date doesn't jibe] the ship entered the port of Tanjung Priok to take Dutch women and children from Japanese concentration camps. In early January 1946 she was ordered to return home, arriving at Portsmouth on 15 February.[2]
The Wiki source is the Service History M/v Prinses Beatrix and Koningin Emma 1939 - 1968. Each ship could carry up to 2000 troops - although the service history does not tell us the number of French troops carried to Saigon:

Via Gibraltar, Port Said, Suez and Aden, the port of Bombay was reached on May 26. First a few trips were made to Trincomalee and a few days after the Japanese had capitulated Emma and her sister ship Beatrix, just arrived, were made part of the operation Jurist the occupation of Penang by the British Marines. Here the British flag was raised and order restored. It had been a long time since the two Dutch ships had worked together. After this sail was set for Trincomalee, where French troops had to [be] embarked, under escort of the mighty French Battleship Richelieu, to Saigon.
The conclusion seems to be that the movement of French forces to Saigon in September and October 1945 was an example of British-French co-operation by air and sea (and two Dutch transports). An interesting little puzzle to solve (after a false start or two - Vietnam War I and II history is a bit of a minefield).

Regards

Mike