If the manager of the shop is an employee of the franchisee, then they would not be likely to be personally liable if the damage occurred in the course of performing their duties, even if it was not related to the specific work being performed on the vehicle.
For instance, consider the situation where engine work is requested, but as a result of some object falling from a height, some panel damage occurs. As long as the manager did not maliciously drop the object, the employer would be vicariously liable for the employee's actions.
Let's turn to the franchisee-franchisor relationship - while it is legally more like an independent contractor relationship, it is both symbiotic and interdependent, and legally independent.1
What would be considered is the actual franchising contract, as well as the substance of the relationship. In unusual cases, a franchisor may be liable for franchisees who act as the agent for them.2
Where a franchisor is considered an employer of the franchisee, then the franchisor can be held vicariously liable.3
Additionally, US case law shows a number of instances where the franchisors have been held liable for negligence in selecting franchisees, maintaining standards, franchise unit design, food safety, and security.4
In the US, the Restatement (Second) of Agency extent of control test imposes vicarious liability on a franchisor that controls (or has the right to control) the day-to-day operations of the franchisee.5
Therefore, a court would request a lot more information pertaining to the particulars of a situation, in order to arrive at a judgement on such a matter.
This information was synthesised from Franchisor Liability for Franchisee Conduct, (2013) Andrew Terry and Joseph Huan, Monash Law Review pp.388-410, page references below. You probably don't need to read all of it, as most of the important information is introduced in the first dozen pages.
1. p. 390
2. p. 390
3. p. 390
4. p. 392
5. p. 394