I will tell you something from my experience and personal understanding off the matter.
First of all, I'd contact the company marketing section.
use your official company email - *no @firstname.lastname@example.org etc..* If I were to write to Ford, I'd use their Contact Form and choose the "Other" inquiry type. Say why I would like to use their intelectual property in my product.
Second of all, there is something called the "fair use of copyrighted material". The film industry would be much different if it wasn't legal to use "normal" cars in movies. The corporations pay to have their product included in a AAA movie - Double-o-7 drives Aston Martin, used to drink Martini now switched to Heineken, wears an Omega Watch, loves Coca Cola Zero, and uses sony electronics products. Of course if you are a small studio, you will reach fewer people, most likely you will not be able to get money directly from the brand.
It is a often found in AAA movie/game productions, where the brands like Coca Cola and Pepsi fight each. So I doubt that you will find a Coke next to Pepsi on "one movie dining table". If you watched some movies you might have noticed that the operating systems used by "the FBI " are usually some crazy tech not similar to Windows or Apple OS. They have been doing that to make sure they wont have legal problems with Microsoft/Apple Corporations. This has changed and in fact now the Corporations want their product to be viewed by the biggest ammount of people. This way most of mobile phones carried on stage by Hollywood movie actors, are Iphones, climbing gear is Petzl and so on.
Another way Around it:
I understand that the shoot will be in real world. With real cars. YOU ARE NOT ALLOWED TO USE THE COMPANY LOGO ON AN INGAME MODEL WITHOUT THE COMPANY PERMISSION. But when it comes to shooting a clip the law is on your side. You can use the cars in movies as long as you own it or have a written permission from the car owner. You could always rent a Movie Prop Car. The digital form of the game object is the bitter part because you do not own the "idea of the car" where the movie situation is clear that you are in possesion of that car you film. You can always make a car similar to the car from the movie you shoot, accept with no logos + you should mess a bit with the proportions and they wont be able to say that you stole the car concept from them, as it will be a technically different, yet similar model.