Ultimately, the liability lies with the driver. Liability coverage is usually provided by the car rental company as part of providing the rental. They are indemnifying the driver in that case. However, in this case they may deny coverage because the driver was in violation of the rental agreement. That is a matter between the driver and the rental car company.

Enterprise itself is not liable. Their liability coverage is indemnifying the driver against financial liability to a third party (you) in case of an accident.

The unfortunate answer is you may need to go after the driver directly. It is up to him to get Enterprise involved and try to get them to indemnify him. If you had collision coverage, your insurance company would subrogate against the driver and collect for their expenses as well as your deductible. Insurance companies are experts in subrogation, it happens all the time, and they can easily cut through any confusion as to financial responsibility. They would be coordinating directly with the driver and the department handling claims for Enterprise (they'd know how to contact them directly).

It is unfortunate that the driver is young and is likely low on financial resources. He may be able to involve his own car insurance company if Enterprise denies coverage. Coverage follows the car, but the driver's own insurance is usually secondary to the vehicle's owner. So if coverage is denied, ideally they should step in as secondary, although the contract violation may give them an out as well, because he was not really in legal possession of the car.

Bottom line is you need to start with the driver here. Contact him as soon as possible, at least partly because if you can get his own insurance involved, they can deny coverage on the basis of "timely filing" if not notified of the accident. On many policies that limit is 60 days.

Hopefully, the damages are within small claims court limits, so you can proceed against him legally without having to retain an attorney, should it come to that.

Unfortunately, there is a very good chance you will not be able to collect here and will have to eat the repair bills. The only silver lining is the driver is a US resident. If they were Canadian, you'd likely be completely SOL.