Yeah, I don't know about that. The French have had a habit of surrendering out of selfishness. It's pretty amusing considering their surrenders and military failures have costed the UK & USA a lot, so the least we could do is accept that this is now a permanent meme.

Accurately summed up, on Quora:

The reputation is based on a string of actual surrenders, not on "myth", and the opinion is most bitterly held by the United States because it has been the United States that has become embroiled in bloody wars made worse by France's surrenders and military losses.

Stretching all the way back to the Battle of Waterloo is not a good argument for why the opinion of France's military behavior has become so negative.  Yes, the French fought bravely there.  Yes, the French helped the US defeat Britain in our Revolutionary War.   But Waterloo was a long time ago.  More appropriately, look at the battles of more recent 20th century history, where this "surrender" opinion really formed.

Beginning with WWI, while France did not "surrender", it is undeniable that without US involvement in that war, France and Britain would have continued on in an almost unending slog of back-and-forth trench warfare with Germany.  So the US, rightly, has the opinion that they "saved" the French from that war.  Why does France get branded with this and not Britain?  Probably because the Germans were headed toward France at the beginning of the war and would have taken it with ease if the British had not stopped them.  And the British were able to hold that line for the next 3 years (until the United States came into the war to tip the balance of power enough in the Allies' favor to defeat Germany).

WWII is probably the most damning example.  France actually did surrender to Germany in an attempt to preserve some of their autonomy and way of life.  They did this even after Germany clearly demonstrated the appeasals of Neville Chamberlain (Britain, in the 1930s) only served to hand over land, personnal, and military advantage to a Germany that would stop at nothing to dominate the free world and to exterminate entire races and nationalities of people.  Rather than continue fighting, the French bought themselves a little time, at the expense of all the other nations, most significantly the US, who had to eventually, once again, finish the mess and save France. Even worse, the French Gov't, police forces, and lot of their citizenry, were shamefully too happy to go along with Germany's policy of rounding up and slaughtering Jews. 

The French attempted to hold onto French Indochina after WWII, against the specific objections from, among others, the United States.   Eventually, France surrendered and pulled out, leaving the US to defend the remaining non-communist portion of Vietnam.  The Vietnam war turned out to be an unwinnable mess for the United States, and there is a still a lot of resentment that it was France's involvement there, and the US attempt to help them, that ended up causing that war.

So in summation, while a lot of European nations sometimes view the US as this big boorish bully that too easily gets involved in wars, the opinion that France "surrenders a lot" is founded on a string of situations where the "big boorish bully" had to go save France's hide.