It depends. Employers are not liable for all the bad acts of every employee at all times. To pursue a civil case against an employer, you must be able to show the driver was working within the scope of their employment at the time of the accident. If the at-fault driver was working on the behalf of their employer when the accident occurred, their employer might be liable.
A personal injury lawyer will be able to review your specific case details and determine if the employer can be held liable for your accident with an employee/company vehicle.