I had the feeling the car was being lifted up due to the air currents.
Yup. It is a bit similar as in a plane wing: In a wing, there is an airflow below the wing, and another airflow above the wing. The wing is curved so that the air flowing above needs to travel a longer path, therefore it travels faster. Faster travel translates into lower pressure, therefore there is a pressure differential which lifts the wing up.
This is similar for a car, which is curved as well. Only, because the bottom side of the car is relatively close to the ground, there is less airflow which increases the pressure differential upwards.
This aerodynamic feature is also the reason why racing cars have features which cause that the airstream presses them into the ground. Without that, it would be easy to lose control.