c. 1300, derken, "to make dark or darker, deprive of light;" early 14c. (intransitive), "to grow or become dark," from dark (adj.) + -en (1). The more usual verb in Middle English in both senses was simply dark, as it is in Chaucer and Shakespeare, and darken did not predominate until 17c. The Anglo-Saxons also had a verb sweorcan meaning "to grow dark."
Meanings "grow less white or clear, turn a darker color" and "render less white or clear" are from late 14c. Figurative sense of "render gloomy, sadden" is from 1742. To darken(one's) door (usually with a negative) "enter one's house as a visitor," usually with an implication of unwelcomeness, is attested from 1729.
1650s, "melancholy," from French chagrin "melancholy, anxiety, vexation" (14c.), from Old North French chagreiner or Angevin dialect chagraigner "sadden," which is of unknown origin, perhaps [Gamillscheg] from Old French graignier "grieve over, be angry," from graigne "sadness, resentment, grief, vexation," from graim "sorrowful," which is perhaps from a Germanic source (compare Old High German gram "angry, fierce").
But OED and other sources trace it to an identical Old French word, borrowed into English phonetically as shagreen, meaning "rough skin or hide" (the connecting notion being "roughness, harshness"), which is itself of uncertain origin. Modern sense of "feeling of irritation from disappointment, mortification or mental pain from the failure of aims or plans" is from 1716.
The town of Chagrin Falls in northeastern Ohio, U.S., was founded 1837 and named for the nearby falls of the Chagrin River. The source of the river name is uncertain; it might be a corruption of Seguin, the name of a Frenchman who is said to have established a trading post nearby in the 1740s.