Looking at France's military history, it doesn't seem terrible. They had some catastrophic moments certainly (Napoleon's invasion of Russia and the existence of Vichy France come to mind), but those are easily offset by their great moments (their performance in the First World War, their role in the American revolution, and their victories against just about everyone during the First Republic for example).
Where and when did we start to look at France as a military embarrassment?
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Essentially it came about as a result of the Fall of France. The Simpsons has Willie the Groundskeeper calling the French "Cheese Eating Surrender Monkeys" in c. 1995, so somewhere between 1945 and 1995 the stereotype, a blatantly wrong and horribly simplistic stereotype, came to be.
Too add to this. The French Military has a long and respected history. However, Several Major Military conflicts in succession, occurred which created the new stereotypes of the French military being inadequate and in capable.
Franco-Prussian War Proved to be a great embarrassment to the French Military. and the beginning of the the stereotype.
World War 1 Only fueled to this, although France fought valiantly, Frances inability to properly adapt to new tactics and uniforms caused a great deal of damage to french military prestige fueling the stereotype of French Military incompetence, Especially compared to the boastfulness of the French Military prior to the war. This was further fueled by the Allies inability to push German Troops out of French Territory.
World War 2 Was probably the greatest French Military disaster which fueled the perception of French incompetence. German Forces taking the totality of France in 6 weeks fueled by the incompetence of Free French Forces. This was capped with the Americans being given the titles of "Supreme Allied Commander" and Generally taking over the position as the leading force of the Allies,A title held by the French during world war 1.
After the War the French embarked on several military expeditions to reclaim the empire,which proved highly disastrous. The French Government was unable to come to grips with France losing its empire, and the French Military, already stretched to the breaking point, lost battles on almost every continent, capping Frances now dismal military record in the modern era. These include French Algerian War,1st Indo-China war,and Suez Crisis.
This prolonged sense of military failure lead to the reputation the French Military has today and while there are some French victories from the time period from 1870-present, they were usually in ancillary conflicts.