1530s, "slight offense taken; feeling of displeasure, resentment, etc. arising from wounded pride, vanity, or self-love," from Middle French pique "a prick, sting, irritation," noun of action from piquer (see pike (n.1)).
Pique is more likely to be a matter of injured self-respect or self-conceit ; it is a quick feeling, and is more fugitive in character. Umbrage is founded upon the idea of being thrown into the shade or over-shadowed ; hence it has the sense of offense at being slighted or not sufficiently recognized; it is indefinite as to the strength or the permanence of the feeling. [Century Dictionary]
"to nettle, irritate, offend; stimulate to action by arousing envy, jealousy, etc., in a slight degree," 1670s, from French piquer "to prick, sting" (see pike (n.1)). Softened meaning "to stimulate, excite" is from 1690s. Related: Piqued; piquing.