It seems bizarre that in the Cold War context, the French government would be so intransigent over their colonies when everyone else in Europe was giving them up. How serious was de Gaulle's threat?
A disclaimer before I start: I have not seen the documentary in question. Being in Europe, I have no access to PBS.
I am not aware of the particular instance that the documentary refers to. Without having seen it, I believe that the documentary might be referring to this quote from De Gaulle: "We do not want to become Communist; we do not want to fall into the Russian orbit; but I hope that you do not push us into it."
In 1945, France emerged victorious from the Second World War. It had been defeated, humiliated, occupied and been the place for some of the most gruesome fighting in the Second World War, but it has come out on top nonetheless. The experience of the Second World War is incredibly important to understand why the French leadership cared so much about retaining their colonies. To us today, it might seem silly why they'd grasp onto colonies and wage war for over 10 years after having spent years already fighting in one of the largest wars the world had ever seen. But that's because we know how it ends. We know what happens in 1954. That hindsight makes it difficult for us to place ourselves in the shoes of those who argued for France to reoccupy Indochina after 1945.
But first, let's wind the clock back to World War 2 and see what led to Charles de Gaulle uttering those words.
On August 14 1941, Franklin Roosevelt together with Winston Churchill released a joint declaration that was to be known as the Atlantic Charter. In the context of Indochina, the sixth clause is the most important one: "After the final destruction of Nazi tyranny they hope to see established a peace which will afford to all nations the means of dwelling in safety within their own boundaries, and which will afford assurance that all the men in all the lands may live out their lives in freedom from fear and want.”
This charter, alongside its sixth clause, had a tremendous effect in the world and while Winston Churchill was quick to reassure his government that the charter did not apply to the British Empire, Roosevelt had meant for it to apply universally. FDR had entered the 1940s with a strong anti-colonialist conviction. This of course extended to the belief that France should give up French Indochina (modern day Vietnam, Cambodia and Laos). FDR felt very strongly about the possibility that Indochina had been used by the Japanese as a springboard for the initial conquests in 1942 (it hadn't) and adding onto his generally bleak opinion about the French after its defeat in 1940, made him very determined to speak out against French colonialism in Indochina.
This does not mean that Roosevelt saw Indochina was being prepared for independence. Roosevelt had at occasions displayed, in the words of Fredrik Logevall, a "patronizing and cryptoracist view of the Vietnamese" and considered them unfit to rule themselves. Instead, he suggested a more paternalistic suggestion in which a trusteeship would be established along the lines of the mandate system of the League of Nations. These former colonies would be helped to independence through a series of stages culminating in total independence.
Roosevelt was very reluctant in allow Free French regular forces to return to Indochina and while he began to look the other way as Free French forces were deployed with the help from the British towards the end of his own life (and the war), Roosevelt still remained convinced that allowing France to return to Indochina was a bad idea - even though it began to falter due to the realities of the war itself. To Roosevelt, the final (and inevitable) goal was universal decolonization.
It is in this context that Charles de Gaulle, after being questioned by Jefferson Caffery, the US ambassador to France, says the quote above. But why? Why did Charles de Gaulle and other French leaders want to hold on to Indochina so badly?
The reason lies in the understanding of the place of colonies in the might of a nation. France wasn't simply France the nation-state but also France as in the French Empire. In 1945, we have yet to see the decolonization that was to come. From this understanding, what made France powerful, what gave it its might and its place amongst the world's leading power, were its colonies. For a nation that was suffering from economic issues after a destructive war, being able to hold on to their colonies might make it possible for them to get back to their feet due to the financial rewards there were to reap from the overseas colonies. Furthermore, there were also cultural and social aspects in the form of the French civilizing mission (mission civilisatrice). French was "responsible" for "civilizing" Indochina. This meant exporting French institutions (and French jobs) to Indochina with a paternalist and condescending view towards their colonial subjects. If France was to step up from their humiliation at the hands of Germany, regain its prestige and become what it was before the war then all of its colonies had to be reinstated.
Therefore, de Gaulle's statement needs to be seen in this context. What de Gaulle is effectively saying is that "if you don't let us reclaim what is rightfully ours and make France great again through the reconquering of our lost colonies then metropolitan France will be so weak that it will be an easy prey for communism". The United States needed France as not only an ally but also as a powerful bulwark against the the apparent Soviet threat coming from the east. The United States needed a sympathetic and stable France to, in the words of Logevall, "fully secure in peacetime the hard-fought victories of the battlefield". This would come to develop in many ways, including the famous Marshall Plan and in the long run, United States support for the French Indochina War.
For the United States, the choice was between a stable, powerful and friendly France on the one hand and the establishment of an independent Vietnam according to the sixth clause of the Atlantic Charter on the other. In the context of late 1945, the choice made sense to those who made it: The United States needed France.