As a country though, France is often known as cowardly for how they reacted/contended/were defeated in both world wars as well as other various wars.

As a first point of clarification, France was not defeated in the First World War. It was invaded, and parts of northern France were occupied for over four years, but the French government and military remained as belligerents until the German armistice. The French military fielded over 8 million servicemembers (about equal to the British Empire and more than anyone else except Russia), and lost about 1.3 million killed in action (more than any other Entente or Allied member bar Russia). The peace treaties for World War I were signed in France, and France was one of the "Big Four" victor powers (the others being the US, UK and Italy). It had the largest army in Europe after the other Entente powers demobilized, and Germany was disarmed.

As for the Battle of France in 1940: I can't speak to the history of the "French surrendering immediately" trope, but it's worth noting that it was a massive campaign of manuever that in 46 days resulted in 25,000 German dead, 85,000 French dead, and hundreds of thousands of wounded. The Germans were victorious largely through better through better use of their air force and tanks, because of their strategy, because of issues of French and British military doctrine and issues of coordinating two countries' militaries, and through plain luck.

However complicating factors were that France was extremely politically divided in the late 1930s, which made it difficult to unite national leadership during the crisis, and the fact that French losses in World War I had a heavy impact on how it behaved at the beginning of World War II, from favoring static defenses (which was a smart money move 25 years earlier), to manpower shortages caused by the demographic imbalance of a lost generation, to France's logistics being crippled by a massive refugee crisis as French civilians fled the invasion zone in massive numbers (with memories of World War I, few wanted to be near such a frontline, and less wanted to be under German occupation, as it was actually harsher in 1914-1918 than German occupation in 1940 proved to be).

As for other wars the French military fought in, I'm not really sure which ones would even contribute to this idea.

Just as an additional World War II note: Despite America's own popular hagiography, the United States government considered that its own public had a very low tolerance for military sacrifice. For instance, the Battle of Tarawa in November 1943 saw 1,700 Americans killed to 4,700 Japanese killed in four days of fighting, and resulted in a total American victory, but the government tried to suppress and censor media reports on the battle because the American losses were considered too shocking. Likewise, the Allied High Command seems to have had a relatively poor opinion of US troops in the 1944-1945 Northwestern European campaign, as many of these were draftees who were considered of low quality and poor morale, who did not want to needlessly fight in a war considered almost over. This is one of the reasons why Eddie Slovik was made an example of by being executed for desertion, the first and only US soldier to have been thus executed since the US Civil War.

Sources: Mostly drawing on Anthony Beevor's The Second World War for the US military section.

And John Keegan's The First World War and The Second World War for WWI info and Battle of France info respectively.

As a follow up question, did the fact that a sizable portion of the French leadership collaborated (thinking of Petain and Vichy France) help amplify this stereotype of the surrendering Frenchmen?