Reposting my previous answer because the original thread was removed by the user.

Great question. It is a bit broad in appeal, so we have to maybe break it down into several smaller questions. It is of course going into alternate history (which I love), but we need to rationalize the OTL questions that stand beneath it, which are:

1. What even is "Vichy France"?

2. How dependent upon Germany was Vichy France?

Okay, so to answer the first question:

Vichy France is the term that historians commonly apply to the national entity that was present mainly in southern France, but also in Syria, Northern Africa and other former French colonies, from 1940 (July 10th: The National Assembly of the Third Republic grants extended powers to Premier Minister Philippe Petain) to 1942 (November 10th-27th: The Germans and Italians execute Case Anton, the military plan to integrate the up until then unoccupied southern France into their northern and south-eastern French occupation zones). De jure, Vichy France existed up until 1944 after that (when France was restored as a democracy by the invading western allies), but had all but vanished when speaking about actually relevant political decisions.

The (nick-)name Vichy France comes from the fact that, while Paris was officially the capital, Paris was under German occupation, so Petain and his cronies chose the small holiday resort village and spa Vichy (in the southern zone) as a capital city to run their government instead.

Important note: The name Vichy France is mostly an invention politically biased towards the western allies to legitimize the "Free French Forces" as the true France. By all reasonable definitions, Vichy France WAS France, whereas the FFL were not much more than a warband of foreign legionnaires inside the British-American armies, even though some colonies like Chad decided to join them. Still, I will continue to use the term "Vichy France" and will try to use "Free France" (again, a term that can be argued has a biased reading of history) for the rebels where necessary. That way, it will be easier for everyone to understand what I am saying.

So the following is what I shall define as Vichy France for the purpose of this question: June 10th, 1940, until November 10th, 1942. I will forego the possibility of an earlier Case Anton due to French autonomous behavior, as this is clearly straying too far into the area of alternate history speculation, something that we will have enough of already. I will also ignore the possibility of Free France and Vichy France allying and Vichy France joining the allies. Again, this would go too deep into the possibilities of alternate history fiction.

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So let's move on to the perhaps more difficult second question. Just how much of a "puppet state", as it is often asserted, was Vichy France really?

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How economically dependent was Vichy France on the German Reich?

I recommend to you Kenneth Mouré's "Economic Choice in Dark Times: The Vichy Economy". A in my opinion great write-up of various historians' work on the topic. You can find it in what I believe is its entirety here. Also, it is pretty much the only source I have for you that is not in the German language, so some additional reading might be had here.

Philippe Verheyde (one of the better historians on the topic out there, even though his works rarely make it past the French language barrier) writes: "In the wake of shattering defeat in 1940, the Vichy regime’s aspirations to reorder French life were nowhere more apparent, and their illusory basis and practical failure nowhere more striking, than in economic policy and performance. Economic contraction and material shortages dominated French life during the German occupation."

Verheyde also notes that the massive shortages under occupation (including food, fuel and clothing) brought the citizens' blame to the Vichy Government. Basically, the French population blamed the lack of what can be argued to be basic resources on the French collaborationist government and by extension on the German forces.

It can also be said that there was a massive amount of economic control coming from Berlin. Vichy France had what was called a Planned Economy by contemporaries - but the term fails to show that this economy was not planned by Vichy, but largely shaped by Berlin's demands, both political (especially Aryanization, I will get to that in 2.2 (even though Aryanization of businesses is very much also an economic demand)) and economic.

Vichy France was very much possessed a classically fascistic approach to economic policy, with a corporatistic spin on legislation and monetary policy - but without the autonomy from Italian and German occupiers that would have been necessary to make the state capitalistic corporatism work in the slightest. German officials had full oversight over and insight into Vichy French economic decision-making, from the ministry of finance to the currency policy. Vichy France continued to use the French franc as its currency, but redesigned using its motto and symbol and put into a fixed exchange rate of 20 Vichy French francs to 1 Nazi German reichsmark.

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Conclusion

To finish it off, Vichy France had few natural resources for its own use to speak of (and no financial assets to produce them even if they did), could not provide for the necessary basic needs of its citizens both because of its own economic instability and the tight grip by the German occupiers and it had a currency that was not kept alive due to Vichy French economic prowess but was instead basically an outpost of German economic policy - much like Vichy France as a country as a whole.

At this point, I might already stop. The answer to your question is no. Vichy France would have been unable to provide for itself.

You can look at Vichy French military efforts in North Africa if you'd like in order to understand the (somewhat fabricated) reason the Axis Powers invaded, claiming that Vichy France violated the armistice by not honoring its neutrality through a perceived surrender to Anglo-American forces.

You can also look at Vichy France's willing cooperation in the Holocaust. Vichy France, to the surprise of even the SS and their cronies, willingly adopted racial policies, persecuting Jews, immigrationgs, freemasons and communists, a group of groups together called the "internal foreigners" or the "Anti-French".

This is of course a point where, yes, the French could have collaborated less - because there was little control we know of coming from the SS leadership and similar institutions tasked with carrying out the Final Solution and other Holocaust- or genocide-related German operations. Vichy France is somewhat similar to Hungary in that respect.

That said, I am here if you have any questions regarding that, but I believe that your question is mainly economic in nature.

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Sources:

Rousso, Henry: "Vichy: Frankreich unter deutscher Besatzung 1940-1944", 2009

Mouré, Kenneth; "Economic Choice in Dark Times: The Vichy Economy", 2007

Piekalkiewicz, Janusz: "Der Zweite Weltkrieg", 1987

Wucher, Albert: "Marksteine der Deutschen Zeitgeschichte 1914-1945", 1991

Zentner, Christian: "Der Zweite Weltkrieg", 1981

Zentrum für Militärgeschichte: "Das Deutsche Reich und der Zweite Weltkrieg", 1979