Every business records transactions into an accounting system. Most small businesses work with a CPA and some accounting software such as Quickbooks to do this. The journal entries for a franchisee or franchisor are no different than for any other business, except that franchise systems deal with some contractual transactions such as royalties and advertising requirements that non-franchised businesses don't.
Make general journal entries. Every business records its transactions and activity in a general journal. The transactions that are entered in a general journal get posted to ledgers and reconciled to bank statements. Journal entries are the most basic accounting entry for any business.
Royalty payments and franchise fees are paid by franchisees and recorded as revenue for a franchisor. Royalties are a business expense for a franchisee, whereas the initial franchise fee is an intellectual property purchase that must be capitalized and depreciated on the company's balance sheet--it may not be expensed in a single year. Franchisors record all of these payments as sales revenue.
Other contractually required payments in a franchise system may include advertising expenditures and/or membership in industry organizations. Many franchisors will request that franchisees submit a set of their accounting records as proof of their compliance with the franchise system. It is important that entries made to comply with these rules are made clearly so that the franchisor can easily see that you are in compliance with the franchise agreement.
Have you CPA or accountant do the depreciation calculations and journal entries for depreciating the franchise fee.