#google is backing you up on this (via @oldguardians)
I realize, looking back on this post, that regular readers of my blog may have thought I made this up. Making up a ridiculous etymology is certainly the sort of thing I might do; in fact I've been meaning to start a sideblog dedicated solely to sufficiently accurate etymologies, and have a notebook with dozens of them jotted down, I just haven't had the time to do anything with them.
But I want to stress that this is not one of those cases. This is, to the best of my knowledge, the very real etymology of the phrase "curry favor".
The Old French fauve or falve referred to the light-brown color that's sometimes called "fallow" in modern English, but since it also sounded similar to faux, meaning "false", it was also associated with deceit and trickery ; the idiom estriller Fauvel literally meant "to groom the fallow one" but idiomatically meant "to lie or trick people".
Then in the 1300s we get the French poem Roman de Fauvel, a satirical poem about a fauve horse, whose name is derived both from the color and from the fact that FAVVEL is an acronym of Flaterie, Avarice, Vilanie, Varieté, Envie, Lascheté (Flattery, Greed, Vileness, Fickleness, Envy, and Cowardice) - all the different vices that this horse embodies.
Fauvel (purportedly modeled after Enguerrand de Marigny [source], an advisor to King Philip IV) is a sinful, conniving, and very rich horse who has various religious and secular leaders fawning over him and brushing him; it was well-known enough that "grooming Fauvel" came to mean "sucking up to someone powerful" more than just "being evil", and when it was translated into English the grooming was translated as currying, which specifically is grooming a horse with a curry comb [wiktionary]. From this we got the Middle English expression "currying Fauvel", which then mutated via folk etymology (in the "reinterpretation of unfamiliar words as more familiar ones" sense, not the "people are wrong about etymology" sense) into "currying favor".
Wiktionary: https://en.wiktionary.org/wiki/curry_favor
Merriam-Webster: https://www.merriam-webster.com/dictionary/curry%20favor
Etymonline: https://www.etymonline.com/word/curry