Listening to Qur'aan in the car is a righteous deed and a beneficial act of worship. But having the speakers directly next to one's feet in such a way that the sound of the Qur'aan is heard from below is something that is not appropriate and you should limit it to the rear speakers if you have any, or do something to change the position of the speakers.
Shaykh Ibn ‘Uthaymeen (may Allah have mercy on him) was asked: In some cars the speakers are level with the feet, and feet or shoes may be placed on the speaker. My question is: when playing Qur'aan, is there any disrespect to the Book of Allah in doing this? Is this comparable to your fatwa against those who stretched out their feet in front of the Book of Allah? We hope that you can advise us, may Allah preserve you.
He replied: If the speakers are beneath the feet as described or are level with the feet, then you should not play Qur'aan, because the fact that the Qur'aan is being heard from beneath a person’s feet is undoubtedly a kind of disrespect towards the Qur'aan. If a person must listen to Qur'aan, then he should lift the speakers above the level of his feet.
End quote from Liqa’ al-Baab al-Maftooh, 57/13.