From where does the phrase "to curry favour" come?

Both words in the phrase "curry favour" need some careful thought.

The usual association of the word "curry" is with Indian food, but not here. Nor is it an adaptation of the English word "carry", or the word "corrie" (used to describe a hollow on a hillside). The origin of the word "curry" here is the Old French verb "conraier" meaning - "to prepare", "to put in order". This is the same source as the name for the rubbing down and dressing of horses – curry combing.

“Favour” here is a corruption of the word “Fauvel.” Fauvel is the antihero of the 14th-century French allegorical verse romance “Roman de Fauvel”: it is the name of a horse that rises to prominence in the French royal court and is used to satirise the self-serving hedonism and hypocrisy evident in the ruling classes of the time. The name Fauvel can be broken down to mean "false veil" in French, and also forms an acrostic F-A-V-V-E-L with the letters standing for the human vices: Flattery, Avarice, Vileness, Variability (Fickleness), Envy, and Laxity.

In the “Roman de Fauvel” church and secular leaders make pilgrimages to see the famous horse and bow to him in servitude. These potentates condescend to brush and clean -- to "curry" Fauvel from his tonsured head to tail. The romance thus gave birth to the English expression "curry fauvel", the obsolete original form of "curry favour".