Is taking a portion of the profits from a car rental, then having the paid amount refunded and relinquishing ownership of the car to the partner after a specified period, considered usury (riba)?

This transaction is a loan that draws a benefit, which is the very essence of forbidden usury (riba). Scholars have agreed that if a lender stipulates an increase or a gift in addition to his loan, then taking that increase is usury.

If you both desire a permissible transaction, you can jointly own the car and rent it out, with the rental income shared between you according to your agreement. Then, the partnership can be dissolved by one of you paying compensation for the other's share.