If it wasn't for the French's substantial assistance during the War for Independence, there may be no America. The United States' help in WW1 and WW2 returned the favor for France.
Many Americans ridicule the French for being cowardly and pretentious snobs while many French think Americans are devoid of culture, inferior, brutish and crass.
France and the United Stated didn't help each other out of some deep affection for one another. It was geopolitics.
hi! perhaps someone can contribute on the other points, but FYI, there is a FAQ* section on the American "French coward" trope
Reputation of the French military (origin of the "surrender monkey" cliché)
*see the link on the sidebar or the wiki tab