Yes, he is being sarcastic. I think that song came out in 1965. There was a fair bit of tension in the US-French relationship by the mid 1950s. Washington and Paris were had disagreed over decolonization, particularly in Indochina. France and Charles de Gaulle in particular were eager to overcome the humiliation of their defeat and collaboration during WWII with Germany. De Gaulle argued the first step was resurrecting their empire. This was unpopular with FDR and others who saw French colonialism as one of the worst varieties of imperialism and genuinely disliked de Gaulle. By the early 1950s American policymakers felt that in trying so hard to keep their empire (re-branded as the gentler French Union) the French were simply pushing decolonized peoples into the Soviet bloc and thus jeopardizing the West's credibility.

Shortly after the French decision to withdraw from Vietnam (which Washington saw as France simply giving up, rather than pursuing a military victory) France joined the British invasion of the Suez canal. President Eisenhower opposed this action, dealing them a humiliating public defeat. At this time, French leaders expressed their displeasure with the dominance of Washington by singling out their large role in the North Atlantic Treaty Organization that covered Europe. De Gaulle began pulling French forces out of the combined NATO command and proclaimed France would need to defend itself. In 1966 he requested NATO troops (eg American military personnel) to leave France. Dean Rusk, LBJ's Secretary of State, reportedly asked if the US soldiers buried in France had to leave too. This was essentially Rusk saying, So do we have to take home the bodies of tens of thousands of American soldiers who died liberating France during WWII? Anyhow, good luck defending yourself without NATO and the US. As you can see no love was lost.

Finally, in 1964 de Gaulle called for the withdrawal of American troops from Vietnam and the neutralization of the Indochina peninsula. Now, keep in mind De Gaulle was responsible for sending French forces to invade Indochina after WWII and re-establish their colonial domain. As you can expect, Lyndon Johnson and the rest of his advisors didn't welcome De Gaulle's public criticism (they would probably say political grandstanding) on American policy, particularly since de Gaulle and France's desperate attempts to resurrect colonialism were responsible for creating the situation in Vietnam.