A “restaurateur” is a person who runs a restaurant; the term is neither masculine nor feminine. A “restaurateur” who is a woman is frequently called a “restaurateuse,” but dictionaries such as the Oxford English Dictionary and Merriam-Webster do not include this word. “Restaurateuse” borrows its feminized ending from words such as “chanteuse” and “masseuse.”

“Restaurateuse” has been cited in print since at least 1842, but was rarely used in the 19th century. In 1947, Lynn Gilmore, a New York restaurant owner and a former model, was chosen as “America’s prettiest restaurateuse” by the National Restaurant Association.
 
   
Wikipedia: Restaurateur
A restaurateur is a person who opens and runs restaurants professionally. Although over time the term has come to describe any person who owns a restaurant, traditionally it refers to a highly skilled professional who is proficient in all aspects of the restaurant business.
 
Etymology
The French word restaurateur comes from the Late Latin term restaurator (“restorer”) and from the Latin term restaurare. The word restauranteur, traditionally considered erroneous, is borrowed from the term restaurant.
 
Merriam-Webster Dictionary
res·tau·ra·teur noun \ˌres-tə-rə-ˈtər\
Definition of RESTAURATEUR
: the operator or proprietor of a restaurant
Origin of RESTAURATEUR
French restaurateur, from Late Latin restaurator restorer, from Latin restaurare
First Known Use: 1796
     
Google Books
1842 (Vol. XIII), The British and Foreign Review, or. European Quarterly Journal, pg. 371:
... like old French people who lose their good looks, they become better cooks : no partridge-stew ever dressed by Ude tastes like one concocted by a gipsy restaurateuse.
(Review of The Zincali; or, an Account of the Gipsies of Spain by George Barrow—ed.)
 
Google Books
Recollections
By William O’Brien
New York, NY: The MacMillan Company
1905
Pg. 387:
... hours of exercise; to smoke their pipes, to read their newspapers, to play at hand-ball, or, if their tastes were more sedentary, at chess or dominoes, and to have their meals supplied by a friendly restaurateur (or, as it happened, restaurateuse).
 
20 October 1906, Saginaw (MI) Evening News, pg. 1, col. 4:
FAMOUS SOUTHERN COOK DEAD
Madame Begues, Noted New Orleans Restaurateuse, Passes Away.
New Orleans, Oct. 20.—Madame Begues, for fifty years one of the most famous cooks in the United States, died last night.
 
Google Books
New Designs for Old Mexico
By Henry Albert Phillips
New York, NY: R.M. McBride and Co.
1939
Pg. 108:
Mrs. Thimgren, an old-time American and restaurateuse on the Mexican scene, says: “No class nowadays?”
 
17 May 1947, New Castle (PA) News, pg. 1, col. 2 photo caption:
Cuisine Queen
Lynn Gilmore, New York restaurant owner, is chosen as America’s prettiest restaurateuse by members of the National Restaurant association at New York City convention.
 
Google Books
Knife and Fork in New York;
Where to eat, what to order
By Lawton Mackall
New York, NY:  R.M. McBride
1948
Pg. 66:
MADELEINE’S LE POISSONNIER
121 East 52nd
ELdorado 5-9706
Snug little place whose chatelaine has gathered a host of friends in the course of her career as a restaurateuse.
 
Google Books
Perelman’s Home Companion:
A Collector’s Item
By S. J. Perelman
New York, NY: Simon and Schuster
1955
Pg. 10:
“You bring with you the smell of grease and short-order frying, you — you restaurateuse, youl”
 
Google Books
July 1976, Texas Monthly, pg. 67, col. 1:
It is run with well-intentioned but heavy-handed Prussian discipline by German-born author and restaurateuse.
 
9 May 1986, Chicago (IL) Sun-Times, “Bertucci’s Corner serves diners a square deal” by Don Rose, pg. 53:
But in this case it comes from a young man who proudly wears his “Chef Anthony” knit shirt and tells you his mother, a restaurateuse, taught him how to cook.
 
Google Books
22 December 1997, New York magazine, pg. 49, col. 1:
Soul-Food Survivor
SYLVIA WOODS, restaurateuse
   
New York (NY) Times
Plutocrats’ Retreats; New York
By Peter Benchley
Published: May 14, 2000
(...)
And so, when the time came to visit the hotel’s restaurant, I armed myself with able aides: my wife, of course, a woman of enormous enthusiasms; a restaurateuse who currently oversees a successful bote on 20th Street; a marine-mammal expert, to alert me if any cetacea appeared on the menu, and a degustatrice des vins who has a reputation as the finest renifleuse on Upper Park Avenue.
 
26 April 2004, Los Angeles (CA) Times, “Legislators to Weigh In—Literally—on Obesity Issue” by Patt Morrison, pg. B2:
Students there grow alternatives to junk/fast/fried cuisine. The public-private effort is underwritten by the mother of California cuisine, restaurateuse Alice Waters.
 
Vanity Fair
Elaine Kaufman, Celebrated New York Restaurateuse, Dies at 81
by Juli Weiner 2:40 PM, DECEMBER 3 2010
Elaine Kaufman, proprietress of the eponymous Upper East Side restaurant Elaine’s, died today at 81. Kaufman was also a fixture on the New York literary, media, and intellectual scenes: since its opening in 1963, Elaine’s clientele has included Charlie Rose, David Halberstam, Jules Feiffer, Nora Ephron, and Terry Southern, Tom Wolfe, and Norman Mailer, among others