“Toot and scramble” is a jocular Americanism for the French “tout ensemble” (all together). “Toot on scramble” was cited in 1853 and “toot and scramble” was cited in 1887.
 
American model Julia “Dudie” Baird popularized the “toot and scramble” term in a newspaper interview in December 1897, when she used it to mean “in the all-together” (naked).
 
   
Merriam-Webster Dictionary
tout ensemble
foreign term tout en·sem·ble \tü-täⁿ-säⁿblə\
:  all together :  general effect
   
(Oxford English Dictionary)
ensemble, adv. and n.
All the parts of anything taken together so that each part is considered only in relation to the whole; the general effect (of a person’s appearance, a whole work of art, etc.). Also   tout ensemble n. /tut ɑ̃sɑ̃bl/  [French tout all] in same sense.
1703   N. Tate Portrait-royal Notes 22   There must be, what Painters call, an agreement of the Tout Ensemble.
1823   Byron Don Juan: Canto XIV xl. 135   The ‘tout ensemble’ of his movements wore a Grace.
1879   J. Beerbohm Wanderings in Patagonia iii. 37   A shaggy beard and moustache completed the toutensemble of his really striking face.
       
9 October 1853, The Bell’s New Weekly Messenger

MRS. PARTINGTON, who has been sojourning a time at Cape Island, was much struck by the “toot on scramble” of the bathers; she said it looked as if the Goffs and Randalls had made an excursion upon the Island!

Chronicling America
22 May 1887, St. Paul (MN) Daily Globe, “The Social Spy Aborad,” pg. 18, col. 3:
The set wreath went up and down the wearer like a column of color, and the “toot en scramble” was far from “research,” as Mrs. Florence would say.
 
2 July 1887, Saginaw (MI) Evening News, “Judge Waxem Abroad,” pg. 8, col. 4:
The roads air first class, too, and fer miles through the country they air lined with rows of trees, like avenues in parks, making the toot and scramble (that’s French) very fine indeed.
(Probably authored by American humorist Edgar Wilson “Bill” Nye.—ed.)
 
Chronicling America
6 July 1887, The True Northerner (Paw Paw, MI), “Caps and Belles,” pg. 3, col. 3:
The materials of the robe may be unexceptional, the books natty, the gloves dainty, but to make the “toot and scramble” perfect, the head-covering must correspond.
     
Google Books
February 1889, The Clothier and Furnisher, “The ‘Biled’ Shirt” by the Rev. Jeems Jeems, pg. 59, col. 1:
Arter all dis de toot an’ scramble was so onsatisfactory dat de watch an’ chain, de finger ring an’ sich gimcrackery was necessary
 
Google Books
Proceedings of the Fifty-First Session of the American Institute of Homeopathy, held at Newport, R. I.
June 20, 1895
Philadelphia, PA: Shermand & Company, Printers
1895
Pg. 258:
And mainly so because it does not include, what Trilby would call ” the altogether,” the tout ensemble of the French — or as Bill Nye calls it, the “toot and scramble ” — but which our great forbear, Hahnemann, so grandly designates in his immortal dictum: THE TOTALITY OF SYMPTOMS.
 
Chronicling America
9 December 1897, Wichita (KS) Daily Eagle, “‘Dudie’ Baird Talks of Real Working Models,” pg. 8, col. 3:
“Did I object posing for Mr. St. Gaudens for the ‘Diana of the Garden?’ Not at all. I have often posed for atists in the ‘toot and scramble,’ if you choose to call it that. Serious working artists and models look upon such matters purely from the standpoint of art. Thoughts ulterior to this never enter their heads.”
(...) (Col. 4)
“I did not pose in the ‘toot and scramble’ for these, but in draperies which ‘recall contemporary fashions rather than theclassic conventions.’”
 
New York (NY) Times
BOOKS OF THE TIMES
By John Gross
Published: November 1, 1985
UNCOMMON CLAY: The Life and Work of Augustus Saint Gaudens. By Burke Wilkinson. 428 pages. Photographs by David Finn. A Helen and Kurt Wolff Book/Harcourt Brace Jovanovich. $22.95.
(...)
One of the most engaging minor characters in ‘‘Uncommon Clay’’ is Julia Baird, known in the art world of the day as ‘‘Dudie,’’ the model who posed for Diana’s body. (The head was modeled on Davida’s.) There is a positive touch of Lorelei Lee in the remarks Mr. Wilkinson quotes from an interview Dudie gave to a reporter. Yes, she had modeled for any number of majestic figures in her time: ‘‘The thrones I haven’t sat on are so few that you could count them on your fingers.’’ No, she didn’t mind posing in the nude - ‘‘in the ‘toot and scramble,’ if you choose to call it that.’’ (’‘Toot and scramble,’’ Mr. Wilkinson explains, was a cheerful American garbling of ‘‘tout ensemble,’’ itself the literal French translation of posing ‘‘in the altogether.’‘)
 
Google Books
25 January 1993, New York magazine, ‘The Insatiable Critic” by Gael Greene, pg. 52, col. 1:
The whole Manhattan toot and scramble tumbled in — all the usual gastromaniacs and the affluentials who consider Jojo their neighborhood hangout.