Ford often used animal names as their "code" names for different chassis. The late 70's saw the release of the Fairmont on Ford's "Fox" chassis, which the 1979 Mustang was then built upon...hence the term, Fox Chassis or Fox Body Mustang.
Similarly, their full size full frame car (Crown Vic/Grand Marquis) is called the Panther.
I read in a book somewhere (Sorry, can't remember which one ) that in the mid 70's Ford had hired some chassie engineers from Audi to help them design a world class platform to base thier (at the time) furture car on. "The Fairmont". (OUCH !) Anyway, the Audi design team were the same Guys responceable for the Audi's "Fox" car. The name came from the interdeptmental people at Ford refering to them as the Fox body team. Don't Flame me ,I didn't write the book. I does make a lot of sense though. Audi did have a car in the early 70's called the Fox. Ford was know to bring in a lot of very smart people from all over the world. And the Fairmont, (OUCH !) was the Original Fox body as it was introduced in 1978, one model year before the Mustang Fox body. Dan
I've recommended that this be stickied several times.
Back in the mid-70's, about the time the Mustang II was introduced, Lee Iacocca got his engineers together and gave them an assignment to create a new (for Ford) concept in vehicle production. He wanted to move to "platform" design, where several cars could be built off of one basic pan. At the time Volkswagen was the leader in this concept with their Fox platform, on which they built the Fox, Golf (Rabbit), 100LS and Dasher among others, so the first Ford platform took the name Fox. On it, Ford built millions of Fairmonts, Granadas, Thunderbirds and our beloved Mustangs.
I would highly recommend two books for anyone that is interested in Fox Mustangs: The Official Ford Mustang 5.0: Technical Reference & Performance Handbook : 1979 Through 1993 and Fox-Body Mustang Recognition Guide 1979-1993. Both are excellent sources of true and accurate information about our cars.
On some forums you'll get chastised for saying "fox BODY" as they're actually "fox CHASSIS" cars, since the actual chassis is the part being referred to and it has had several different bodies on it.