Americans used to have an extremely high opinion of France as a result of French help during the Revolution. Before World War II, Americans could probably think of several ways the USA and British Empire could go to war, but the idea of Americans fighting Frenchmen was nonsensical. I'm not sure of French feelings towards America, but I am pretty sure they were positive in general. The US saw France, another democratic republic, as its natural ally and friend in Europe, not Britain.
World War II changed that for various reasons. 1) FDR's distrust of DeGaulle more or less poisoned him towards the US, and given his importance in French politics after the war, France took various actions the US took as insulting. 2) The extremely dependent position of France after the war hurt a lot of French pride, and this was expressed in many ways antagonistic to the US. The economic, militarial, and political dependence of France created an anti-American response as an attempt to restore French power and influence. 3) The French far left, and therefore many of France's intellectuals, became very anti-American because of their loyalty towards Soviet Communism. This moved French attitudes towards America. 4) US and French ofreign policy interests were not the same, and France often found itself on the losing side of what America wanted (in Indochina, Suez War, Algeria).
As a result, France became increasingly anatagonistic towards America. I won't say anti-American because the US and France remained allies and cooperated in many ways, but it was a strained relationship. This in turn, generated an anti-French feeling in the US.
Probably the most important thing to create a US-France special relationship is that France cannot suffer such a large scale defeat as it did in May 1940. A France that could truly say it resisted the Nazis and retained most of its power and influence would make a strong partner for the US during and after the war, even if it weakened. By not being as dependant on the US, it could use its own resources to achieve goals and not be subject to US pressure. France would be more healthy emotionally and refrain from some policies that seemed only to exist to tweak the US. A relationship built more on equality would be a healthier relationship. A France that retained some great power status in its own right would be less likely to resent the US own increased influence.
So essentially you need a very different World War II while still creating a situation where the US and France were major allies in a major war. POD might go back even to a different outcome in WWI or Russian Civil War. Perhaps a world where the Soviet Union was much weakened or whose lands contained multiple countries. Germany would then strike east first instead of west, creating the conditions of a major world war that could suck in the US, but leave France as a viable world power afterwards.