The OED's earliest date of 1939 notwithstanding, the term "blue movie" (usually in quotation marks, as you'd expect a newfangled term to be) appears in the relevant sense in sources from as early as 1923. Strikingly, the three earliest occurrences—from 1922–1924, 1926, and 1931—that I have found all are set in the city of Marseilles.
From G.L. Morrill, Primrose Paths from Paris to Palmyra: Travel Revels in France, Spain, Corsica, Malta, Italy, Austria, Czechoslovakia, Germany, Hungary, Jugoslavia, Bulgaria, Turkey, Greece, Mytilene, Egypt, Sudan, Arabia, Palestine, Syria, Canary Islands, Cuba (1924):
Marseilles hadn't changed much for the better since my visit of two years ago. It still bears the palm for being the "dirtiest" city in France in every sense of the word. I could not escape from an Arab guide who listed the city's agreeable vices from A to Z, and asked if I wanted to see the “blue" movies;, or exhibitions of bestiality, sodomy, incest, and so forth. I thanked him for his interest in me, but told him in American slang that was all "old stuff." Then he proposed the "magic mirror," with which my rounder readers are probably familiar. But enough!
Morrill apparently already encountered "blue movies" in his 1922 visit to Marseilles, to judge from the blurb copy citing highlights from another of his books (Mediterranean Mud: A Winter Tramp Through the Azores, Sicily, Tunisia, Algeria, French Morocco, Spanish Morocco, Spain, France, and Portugal ), advertised at the back of yet another of his books (Near Hell in the Far East: A Pleasure Jaunt Through Japan, Formosa, Korea, Manchuria, China, Tonkin, Cochin-Chine, Cambodia, Siam, Malay States, Sumatra, Java, Madura, Bali, Lombok, Borneo, Celebes, Hawaii ):
Sordid life in Spanish music halls of Seville and Barcelona—Suppressed history of the infamous morals of Spain's royalty—Gipsy cave-dances of Granada—In Lisbon during a revolution—The "blue movies" and underworld of Marseilles—Female cannibals and poisoners of Palermo—Sicily's degraded peasantry, and her crime, poverty, banditry, and immorality—Island love in the Azores—etc. etc.
Unfortunately, the only copy of Mediterranean Mud that a Google Books search turns up doesn't offer even a snippet view of the text, despite the fact that the book is more than a century old.
From "Lambda Chis on European Excursions," in The Purple, Green, and Gold (February 1926):
Tuesday, Aug. 11. We arrive at Aix[-en-Provence] in time for lunch at the Hotel du Palais. We visit the library in the ancient Hotel de Ville seeing the original of [King] Rene's beautifully illuminated Book of Hours and an illuminated letter signed by Rene. The cathedral of St. Sauveur, dating back to the eleventh century, proves to be of unusual interest with its magnificently carved doors, the famous triptych of Rene and his queen and the peculiar "baptistry" with the central altar of Gothic design approached by three steps and surrounded by eight antique Roman columns which are, of course, much older than the church, and which are said to have been taken from a temple of Appolo. We visit the museum and see there a cast of Rene in armour. Take the car to Marseilles where we are accosted by numerous solicitors for theatres, restaurants and hotels. We forego the special opportunity offered by one of them to see a "blue movie."
And from Harry Hervey, The Iron Widow (1931), a novel later republished as She-Devil) [combined snippets]:
When his money was gone he found makeshift lodging on and about the wharves. There he encountered the transient and disreputable population of Europeans, Africans and Asiatics that exists haphazardly and vividly on the waterfronts of all great ports, particularly at Marseilles. His advent among them—a clear-eyed, yellow-haired boy with a curious air of innocence that proclaimed its inaccessibility—would have been a signal for suspicion and derision but for the trust his innate simplicity engendered. And it was his manner of accepting and belonging without being actually a part that permitted him to enter into their midst and mingle unmolested.
His appearance singled him out when tourists visited the waterfront, and he made a little money acting as a guide. His imperturbable manner excluded from those tours any distasteful innuendo. He could watch a "blue movie" without flickering an eyelash yet not appear brazen; and when he convoyed sightseers through the Ditch his casual air gave the excursion the proper atmosphere of intimacy without contamination.
Earlier than all but the elusive Mediterranean Mud occurrence is an instance in which the meaning of the term is somewhat less clear than in the preceding examples. From Hazel Naylor, "Yesterday, Today and Tomorrow," in Motion Picture Magazine (March 1922):
It's a blue world—blue Sundays, blue movies, blue business men and blue matinée girls. Contributive to this indigo eulogy is the news that Marie Prevost, Phyllis Haver and Harriett Hammond have parked their bathing suits forever in mothballs. But even more pertinent to the blues in question is the fact that our pet leading men are developing ambitions to become directors. It is said enough for the tired business man to anticipate a boring cinema evening without his Mack Sennett water babies, but what, I ask you, are we going to do now that our handsome leading men are hiding their romantic eyes behind the camera.
AS nearly as I can gauge the situation here, Hazel Naylor doesn't have pornographic movies in mind hen she refers to "blue movies," but rather something like "sad movies." In this regard it may be significant that she doesn't put the term in quotation marks, as the other three authors from before 1932 do.
Oddly enough, in the United States there appears to have been a guide to movies appropriate for young viewers, called the "Blue Movie Book." From National Congress of Parents and Teachers, Proceedings of the Thirty-Second Annual Meeting, Cleveland, Ohio, April 30–May 5, 1928 (1928) [combined snippets]:
The committee on motion pictures was very active, giving lists of approved pictures thru the bulletin and by mail and urging the use of the "Blue Movie Book" for pictures suitable for children.
The earliest Marseilles-unrelated instance of "blue movies" that I came across is from an unidentified article in Vanity Fair (1933) [combined snippets], where the modern-day Gomorrah is Havana, Cuba:
At night you can wander down in the Chinese Quarter of Old Havana. The inhabitants are oddly at variance with their Manhattan brothers. Here are no stoic enigmas, no amber slinking—but instead laughter and a light touch. You may eat, if you like, ambrosial concoctions of chicken and fresh almonds—as opposed to the monotonous chop-suey standard of American Chinese restaurants—and the proprietor, practically convulsed with laughter, will bring out bottle after bottle and insist on your trying a glass each of rose wine, raisin wine, rice wine and sharp pungent Chinese whiskey—all of which you will do with alacrity, anxious, of course, to do your duty as guests. Afterward, treat yourself to the amazing spectacle of the Teatro Venus, or Shanghai, where practically the entire Chinese population goes every single night to sit and watch in rapt delight the "blue movies" which may be found in almost every section of Havana, and the manufacture of which is a profitable minor national industry.
Treating all of G.L. Morrill's forays into the cinema of Marseilles as a single episode, we still have three instances in U.S. English of "blue movie" in the broad sense of "pornographic film" linked to Marseilles, from 1922 to 1931, with no relevant instances from anywhere else. It seems not unlikely that the purveyors of these entertainments referred to them locally—for reasons unknown—as films bleu, or something similar, and that English speakers who were exposed to them came back to their native lands with titillating tales of "blue movies."
Indeed, an author writing in the 1950s refers to "le film bleu"—although it isn't obviously in reference to sex (as opposed to sexy) movies. From Geoffrey Wagner, Parade of Pleasure: A Study of Popular Iconography in the U.S.A. (1955, evidently reprinted from an earlier version in a 1951 issue of Hollywood Quarterly) [combined snippets]:
A harmonious thematic balance is maintained that makes the presentation logical and inevitable, and infinitely more gripping than the hypocritical eroticism of later Hollywood productions by the same director. Here Von Sternberg created his atmosphere with an almost suffocating use of costume to offset cabaret scenes which are, contrary to front-office opinion, apt to be highly anti-erotic on the screen. This 'le film bleu', which used to be such a diverting addition to the Englishman's visit to France and which we find admirably described in Paul Bowles's Let It Come Down, amply witnesses. If you want to see 'sexiness' killing eroticism, look at nine out of ten of those ovoid faces served up to us in, as it were, the feminine egg-cups of of contemporary Hollywood costumiers.