Did this purchase of a franchise be comprised of only the franchise right? Or, did it include other parts of the business; e.g., furniture, equipment, building, customer lists, etc.? Basically, did you purchase an ongoing business?
If you bought a business that includes various aspects of a complete business, you and the seller must allocate the sales/purchase price to the various assets. The assets are then capitalized and either depreciation or amortization taken on the assets; depending on what category they are in. Franchise cost are Section 197 intangibles, and are amortized over 15 years.
Payments for the purchase of the franchise fee/business are not deductible in and of themselves, as the cost of the business assets/franchise is recovered through depreciation/amortization. However, it sound like you have an installment purchase, then each payment would have an interest component. The interest paid in each payment would be treated as business interest and follow the rules for interest expenses.
Here is a link to IRS Publication 535. There are many links and suggestions for other publications that are very helpful for a small business.
https://www.irs.gov/publications/p535
https://www.irs.gov/forms-pubs/about-form-8594
**Disclaimer: Effort has been made to offer correct information; but due to the discussion forum limitations, the poster disclaims any legal responsibility for the accuracy of the poster's response**
