Sabrina was the last film Billy Wilder made with Paramount Pictures—this way back in the old days, when the studio system was king and directors, actors and studios were all one big happy (or dysfunctional) family.
Wilder had gotten his major directing start at Paramount with The Major and the Minor in 1942, and had directed many of his most iconic films for the studio, including Double Indemnity (1944), The Lost Weekend (1945) and Sunset Blvd. (1950).
So why did Wilder and the studio break up? The trigger doesn't seem to have been Sabrina, but the film Wilder released the year before, Stalag 17. Stalag 17 was a World War II drama; Paramount executives wanted to change concentration camp guards from Germans to Poles, so as not to offend audiences in West Germany. Wilder, an Austrian Jew whose stepfather had been killed in the Holocaust, was really, really upset, and demanded an apology. When one never came, he decided not to renew his contract.
Instead he formed his own independent film company—and had a big hit right away with The Seven Year Itch (1955), one of Marilyn Monroe's most famous films. (In Sabrina the characters talk about going to see the play The Seven Year Itch, which the film was based on.)
Sabrina, then, was the last film that Wilder slipped in at Paramount before heading out the door. It's a film that Wilder would have had trouble doing without the studio, though— Linus and David's home is actually the Long Island estate of Paramount chairman Barney Balaban.