According to Daniel Parton, an associate professor of law at Boston University, in March 1946, the French Government recognised the Republic of Vietnam as 'a free state' but not as an independent one ... having its own 'government, it's parliament, it's army and it's finance.'
Q. What was the difference between 'free state' and 'independent state' that he French government relying upon?
An Independent State is a:
nation, country, or state in which its residents and population, or some portion thereof, exercise self-government, and usually sovereignty, over its territory.
Whereas a Free State is:
occasionally used in the official titles of some states throughout the world with varying meanings depending on the context. In principle, the title asserts and emphasises a particular freedom of the state in question, but this is not always reflected in practice. Some states use the title to assert sovereignty or independence from foreign domination, while others have used it to assert autonomy within a larger nation-state. Sometimes "free state" is used as a synonym for "republic".
One can only surmise without access to the contemporaneous records of the Gouvernement de la République Française but it seems that the reference to Vietnam (or French Indochina) as being a Free State may have been way for France to announce to the world her military, political and/or commercial intentions in the area, and to give the Vietnamese people some degree of autonomy without France relinquishing overall control regained following the 1945 to 1946 War in Vietnam.
For context: the geopolitical events in and around Indochina at the time were complex with changing loyalties, fragile allegiances and contested borders with the main events being the Japanese invasion in 1940, the 1945 coup d'état, the Japanese and Vichy French surrender at the end of the second world war, and the the First Indochina War in 1946, but a more detailed answer may be available at HistorySE or PoliticsSE.
