I disagree with your placement of the French as in an active, coordinated league with all our enemies.
The French are always out for the French, always seeking a role larger than their actual power demands and thus since the end of WWII, and more so since the end of the cold war, the only role that France has found compatible with its own sense of itself is to be an obstruction to whatever the U.S. is trying to do.
If France was not playing the role of an obstructionist, then it would be no more than a weak junior partner in a US led alliance; a role that is commensurate with the true degree of power it deserves. That reality is incompatible with the inflated view it has of itself. Thus it has been since the second German conquest of France.
Such friends have always been more dangerous than enemies, because as they seek a role that is larger than they deserve it places them as an ineffectual, bumbling, obstructing interlocutor between us and our real enemies. In that role of pretending to stand between us and our enemies, they are really just out for themselves and never really representing either our interests or even our joint interests with them. That hurts our ability to obtain our actual joint interests, against our enemies, because our enemies naturally prefer the weaker demands made on them by the weaker party - France. This aspect of our relationship with France can be seen in almost every major diplomatic area throughout the "cold war" and since the demise of the Soviet Union.
France was always seeking a separate peace for the west on France's terms, the Soviets would not reject it but seek our acceptance of France's terms, because without our agreement the terms had no power. We would not agree and France would then proclaim that it had taken the higher ground, when in fact all it had done was convince the Soviets that they ought to hold out against us.
France = self-interest, puffed-up sense of itself, obstruction of an ally of much greater power, myth making of the rightness of its position, selling that myth as a means to purchase more global acceptance of its role as an obstructionist.
By the 1960s, our enemies across the world learned that if they wanted to defeat us diplomatically in international forumns, all they had to do was to play on France's inflated sense of itself and France would discard western multilateral positions for its own self-interest - just to oppose the US, because opposing the US suits its national ego.
Well you disagreed with me, but then made my argument for me. While I do not believe that members of the French government sit down with our enemies, I think that it is in their very nature to knock us down, in order to prop themselves up.
France wishes for the days of old when they were a real power. The only way for them to do that is to obstruct America, as you said, and get the world to look at them as the true peacemakers, organizers, or saviors of the downtrodden or wartorn countries of the world.
They wake up each day and despise us for our comfort, wealth and freedom that we have in America. Every fiber of their being wishes they were in our position.