Green’s Dictionary of Slang

blue adj.3

also azure, indigo
[? bluegown under blue adj.1 , the Fr. Bibliothèque bleue, ‘a series of books of questionable character’ (F&H) or as the opposite of brown adj.2 (1); note the papier bleu which in 18C covered the pornographic or seditious material on the tray of a colporteur, an itinerant Parisian bookseller]

[early 19C+] coarse, obscene, pornographic; thus blue film, blue movie; thus, constr. with the, coarseness, obscenity.

In compounds

blue light (n.)

see separate entry.

In phrases

burn it blue (v.)

[early 18C] to act outrageously, poss. by speaking very coarsely.

make the air blue (v.) (also make the air turn blue, turn the air blue)

[late 19C+] to swear, to use obscenities.