I'm reading rather a good book on the latter part of WW1.
The 8th of August 1918 was described by Ludendorff as " the black day of the German Army in the history of the war.". Indeed, the victory at the battle of Amiens by British, Australian and Canadian forces & the promise of huge numbers of Americans entering the fray brought about the Armistice & German capitulation.
All armies, no matter how good, can have their "Black Day".
The French have had their share. Indeed, you can make a case for many French wars wars beginning with strings of victories before ending in defeat.
So, to be a "Black Day" doesn't mean eventual defeat but a significant military disaster.
I'd like to nominate the battle of the Sedan in the Franco-Prussian War.
The Battle of Sedan, fought from 1 to 2 September 1870. It resulted in the capture of Emperor Napoleon III and large numbers of his troops and for all intents and purposes decided the war in favour of Prussia and its allies (though fighting continued, of course, under a new French government).
Would you like to nominate any other historical defeats worthy of the title, "Black Day" for the French army?