Actually and technically, the French won World War 2 with the allies. Don't forget that they are part of the invasion force into France, that they also participated in the battles of Italy (in fact the Free French Forces in Italy were some of the best troops - but ok, so they were from North Africa). That the French lose in 1940 has more to do with leadership, much of the leadership was held-over from WW 1. Yet, when De Gaulle launches a counter attack using limited (if superior) French tanks against Rommel's Ghost division, he has signficant (if short-term) success.
The problem for the French is not so much bravery, but doctrine. Because of problems between the left and right in domestic politics, the professional officers relied on a conscript enlisted and therefore adopted a defensive doctrrine over the Maginot line. However, that line could have been used offensively, as forward bases.
So yes, the French lose Paris, and for a while they become Vichy France, but in the end the French are part of the force that retakes their home and drives into Germany.
The French also won World War 1 (with a lot of help from the English and much later the US). For the most part it was French troops on the battlefields, and that a good part of a generation lost their lives their should also show that the French are willing to stick out their necks. When the Americans landed, their tanks and much of their supply came from the French and English.
Also don't forget that for a good part of the turn of the 18th Century, France was the dominant power of Europe. The French army conquered just about all of Europe but suffered the problem most empires do- over stretch. Considering that the French seem to be fighting just about everyone in Europe, what the French achieve is not matched until Germany tries it over a century later.
The loss of their colonies in Indochina and North Africa can also be seen as the effect of having just come through a costly war and the inability to confront highly mobilized independence movements when it was still licking its wounds.
Compare that to the French more recently, and the army is more impressive. The French have been fairly effective in their deployments abroad and French weapons are very competitive with US for international sales.
Now when you think about those advocates who support the end of NATO and replacing it with a more European force, what you are talking about is a more militarily strong France tied in union with Germany. Germany has its own constitutional issues with sending forces abroad, but France has a strong hold on to its former empire. With French desires to dominate the EU politically- this is enough for Americans to take the French a bit seriously.
The virtue of the last 50 years or so is that generally the Europeans and the AMericans have had common interests, but there has been a fair amount of competition as well, especially lately. For the smaller countries of Europe, I think you have to ask if you would prefer an over-horizon pax americana or an in-your-backyard pax-franco-germania. I fear you are unlikely to find the same support for your individual autonomy from France as you might the US.
There are good reasons for the French disagreements with the US. Two issues stand out. For one, the French were not as fond of German reunification into West Germany after the Second World War. The French still had bad memories of conquest and saw that the Germans could conceivably do it again. There is plenty of reason to argue that Germany is the dominant state of Europe today. For another the US was very active in putting down communist movements in France after WW 2. (For those who don't know much of the French resistance was communist).
But I think most of all was the Suez Crisis, when the US told France, Israel and England they could not intervene in Egypt for the Suez Canal. For England this meant that from now on they would tow the US line and saw junior partnership status with the US as the best choice. THis makes sense when you consider the importance the English have in international security and international capital mobility. For the US and Israel, it tied the two countries together. But for France, it was an insult and a betrayal. The US was responding in large part due to anti-colonialism - in otherwords against the French empire. But for France this merely meant that the US was trying to remove France as empire for an empire of its own design. Furthermore, the French could not wholly trust the US for its security and certainly not for leadership.
Kharn- if you look at your numbers something doesn't match. You have a lot more "wins" then "loses". I would hasten to aid that the Brits have not been quite so lucky with their colonial wars (although they have not done as badly as the Portugues or the Netherlands).