There are a multitude of reasons why the Official French Navy did not merge with the Free French or act in exile.

• Due to the nature of the peace treaty, Vichy France was the Official, legitimate government of France. There was no 'government-in-exile' like the polish or Low Countries, meaning that alignment to France, meant Alignment to Vichy. (or at least it made a more confusing picture for the French). So the admirals stood their ground and stood by their legitimate government.

• Defeatism, there was a lot of political disunity and defeatist attitude around this time. France, one of the most powerful countries in the world had fell within weeks. Not only was Vichy the official France, but it was saved from the German onslaught by the treaty, and many people saw Germany as a powerful (insurmountable?) enemy that had won them over.

-Right-wing attitudes, up to the war there had been a strong Right wing political presence in France which could easily sympathise with the newly created Vichy France, which was based on many Right wing ideals and national traditions. The navy was an extremely traditional portion of the military and so fitted well within the Vichy Regime.

-Anglophobia, there had been a long tradition of anti-British attitude, especially in the navy, built over a long period of rivalry between Britain and France in the forging of their Globe spanning Empires which naturally requires naval supremacy. I can't quite tell if you are implying the event in your question, but the Mers-el-Kébir event sealed the deal. No Admiral would be siding with the British after such a horrific act. Even if you can see it as a necessary action, put yourself in the shoes of a French sailor, it would turn your stomach.

I don't feel qualified to answer this question, but if anyone is unfamiliar with this incident and wishes to investigate further on their own, the OP is asking about Operation Catapult, which took place in July of 1940, during World War II.

Follow-up questions:

Did the British feel any tangible backlash from this event (from France or another nation) in future stages of WWII, or in future conflicts?

Was there any documented German reaction?

Admiral Rene-Emile Godfroy: "For us Frenchmen the fact is that a government still exists in France, a government supported by a Parliament established in non-occupied territory and which in consequence cannot be considered irregular or deposed. The establishment elsewhere of another government, and all support for this other government, would clearly be rebellion" (Hastings, Max, p. 125, All Hell Let Loose, The World at War 1939–45, Harper Press, London, 2011)

I just watched an amazing documentary about this point in history. It's called Secrets of the Dead: Churchill's Deadly Decision. It's on Netflix, but I was having trouble finding a link.

It is focused on Churchill's decision to attack the naval fleet of Vichy France at multiple points...most notably the attack on Mers-el-Kébir. It's a great doc, the gist of it is that Admiral Darlan promised Churchill that the French Navy would never fall into German hands. This promise wasn't enough after France was captured by the Nazis. Churchill made the decision to forcibly capture/destroy the French Navy so that the ships could not be used in an attack against Great Britain. Additionally, such a forward action by the British showed Roosevelt that the British wouldn't roll over like the French, and were going to fight until the end. The U.S. began sending aid to Great britain shortly after the attacks on French ports.

Has something like that ever happened, with a force defecting from its conquered home country and fighting its new government?