There is a possibility that pique-nique is a nonce word coined to create an impression or image, usually nonsense. Edward Lear’s “runcible spoon” or James Joyce’s “quark” is nonce words. But they had a purpose that is not evident for the anonymously coined pique-nique.
Another possibility is that pique-nique is a portmanteau word that combines two or more words into a new word, such as motel (motorcar and hotel), pixel (picture and element), etc. Lewis Carroll invented this term in Looking-Glass, in which Humpty Dumpty says: “‘Slithy’ means ‘lithe and slimy.’ ‘Lithe’ is the same as ‘active.’ You see, it’s like a portmanteau. There are two meanings packed up into one word.”
Since 1649, the two meanings of pique-nique are is unknown and perhaps unknowable.
Featured Image: John Tenniel. Humpty-Dumpty. Through the Looking-Glass (1871)