Is the franchisee the only party of interest in a breach of contract lawsuit?
What's the real nature of your claim? Generally, if you enter into a contract with a corporation or LLC, your sole recourse is against that company. So if the franchise/company provides auto body parts and you were supposed to receive a muffler (and didn't), usually you can only look to the franchisee for your claim.
However, there could be an unusual situation where although you were a customer of the franchisee, the underlying franchise model is the real problem--not just the service delivery at the franchisee end.
Take, for example, a weight management program. If it made you gravely ill, you might argue that the issue is not just with the franchisee that provided you with the foods and supplements, but with the franchisor who developed them.
But in that situation, you're starting to move past a basic breach of contract situation and into a tort claim.
To get a clear assessment of your potential damages and who you can fairly bring into a lawsuit, you'd be wise to consult with a litigation attorney in your area--particularly one who has experience with franchises and going through the offering circulars.