What's the origin of "qu" in the word "masquerade"?

Solution 1:

The word is derived from Middle French masque (Middle French covers a period of around 1340–1610) which accounts for the -qu- spelling.

Etymonline has

masque (n.)
"masquerade, masked ball," 1510s, from Middle French masque; see mask (n.), with which it was originally identical. It developed a special sense of "amateur theatrical performance" (1560s) in Elizabethan times, when such entertainments (originally performed in masks) were popular among the nobility.

The word as imported into English hasn't changed; it appears that it has changed in French, possibly under the influence of Spanish.