One way of explaining the balloon's behaviour is to recall Einstein's principle of equivalence: a uniformly accelerated system is indistinguishable from a system in which a gravitational field is acting in the direction opposed to the acceleration. So a car which is accelerating forwards is just like a car that's resting on its back windshield with its headlights pointing up into the air -- unsecured objects tend to roll towards the back of the car.
The helium balloon in the car that's resting on its back windshield will move towards the front windshield because of its buoyancy. Therefore, the helium balloon in the accelerating car will also move towards the front windshield, moved by buoyancy forces.
Another way of putting this is to say that when we accelerate, everything in the car experiences a force acting towards the back windshield -- but because the air in the car is denser than the helium in the balloon, it experiences a greater force, and therefore it moves backwards and displaces the balloon forwards.
Another way to think of this is like this. Instead of a balloon, consider a bubble in a tanker truck filled with water (except for the bubble, of course). Since the water is heavier than the air, you intuitively expect the water to be shoved to the back when the truck accelerates. But this means the bubble moves forward. And this is exactly analogous to the helium balloon in your car, because helium is lighter than air. Of course, this still boils down to the same basic principle above: the air experiences a greater force, and therefore it moves backwards and displaces the balloon forwards. Many of us find it easier to visualize with the bubble in the tanker truck.