The answer is: circa 1400! To quote from a previous answer of mine:

In early fourteenth century western Europe, red was the It Color. Cloth merchants sold a lot of it, either as plain red fabric or as "medleys", wools woven with mixed colors, where red predominated. Across Europe, fine scarlet wools could cost as much as silks, even if the wool cloth itself was of the same grade as a much cheaper green, blue, or black fabric. The truest and most expensive reds were made from dyes derived from various Mediterranean scale insects: kermes and Polish and Armenian cochineal. These are bugs that basically look like brown bumps on a twig or a leaf, but dried, powdered, and mixed with water they will turn your boring white wool into something fit for a king. Literally - these red fabrics have been compared to Roman purples.

Starting around the time of the Black Death (1346-1353), the value and predominance of scarlet wools and mostly-scarlet medleys and striped fabrics declined, and those of darker textiles increased. These wool were typically dyed blue prior to weaving with woad, a fairly common dye (in contrast to the expensive imported kermes and cochineal), and then dyed again afterward: with weld to produce green, madder to make some shade of purple, woad again to make a deeper blue, and other dyes to make blacks and greys. In accounts recording high-end broadcloths sold in Bruges, "bright"-colored cloths made up roughly three-quarters of the wools that were bought and sold between 1330 and 1370; these dark wools made up a very small portion until the last few decades of the century, at which point they became a significant minority. The changes started to reverse in the 1400s, but after that we go back to the bright colors decreasing and the dark ones increasing until the latter made up 90% of the wools by the end of the century.

It's very tempting to draw a psychological explanation from this - the dates line up so well. Is it possible that society itself was traumatized from the massive amount of death that occurred in the middle of the fourteenth century? Well ... it seems unlikely. By the time that dark colors became the norm, everyone who had experienced the Black Death was gone. Some other options are that Spanish tastes for black were seeping northward, or that Duke Philip the Good and King René of Anjou's tendency to wear only black and grey affected fashion in general, but these too seem like overly simplistic explanations with little underpinning them except the coincidence of timing. As mentioned earlier, black was no more expensive than any other color and was less expensive than the red produced from kermes and cochineal, so it wasn't really a status marker in terms of conspicuous consumption. We can't come to any definite conclusion on why this happened; all we can say is that black and other dark colors started to become fashionable and then it became a status marker to dress in black, because doing so proved that you were not just wealthy enough to buy the most expensive fabric (as with red) but knowledgeable enough to discern that a color family was "in" even when it wasn't marked out strongly by price.

For further reading, you might be interested in "The Anti-Red Shift - to the 'Dark Side': colour changes in Flemish luxury woollens, 1300-1550" by John H. Munro, from Medieval Clothing & Textiles vol. 3.