Is it franchiser, or franchisor?
Solution 1:
Confusion seems to have arisen between franchiser and franchisee. The "-ee" suffix refers to the one who may accept something and the "er" usually refers to the one furnishing that thing thing (Compare offerer - 2. A person who presents something for acceptance; one who makes an offer or proposal; and offeree - a person to whom something is or has been offered;)
However, confusion was introduced between the -er suffix and the -or suffix. They are normally considered to be the same and implying the agent doing the action (inspector; worker).
As if this were not enough, the law then had mortgagor - the borrower in a mortgage, typically a homeowner., and mortgagee the lender in a mortgage, typically a bank. BUT a mortager -> a person who mortgages property (and hence) the borrower in a mortgage; = mortgagor n. Also occasionally (in popular use): the creditor or lender in a mortgage; = mortgagee n. 2
And so it is with Franchiser and franchiser and franchisee. The distinctions between agent and patient have become confused.
The OED gives
franchiser, n.
Etymology: Partly < franchise n. + -er suffix1, and partly < franchise v. + -er suffix1.
A person in possession of a franchise, [...] or who grants a franchise, esp. (originally U.S.) a commercial one (see franchise n.2e, and cf. franchisor n.).1976 Times 14 Dec. 20/2 Kentucky Fried Chicken, second to Wimpy..as Britain's largest food franchisers, is planning a £1.25m expansion programme.
franchisor, n.
Etymology: < franchise v. + -or suffix. Compare earlier franchiser n. and franchisee n.
A person who or company which grants commercial franchises (franchise n. 2e). Cf. franchiser n.
1990 Reader's Digest Aug. 130/1 Because advertising, training, supply and other services are provided by the franchisor, a franchise has a much better chance of succeeding than an independent company.
franchisee, n.
Etymology: < franchise v. + -ee suffix1. Compare earlier franchiser n. A holder of a commercial franchise (franchise n.2e).
1966 Economist 9 July 148/1 Franchisers, to be successful, must to some degree tell their franchisees what to sell and at what price.
Thus franchiser and franchisee may be the same, as may franchisor and franchiser.
All definitions = OED
Edit to add earliest record of the words:
Franchiser originally meant a person with a vote:
1555 R. Sherry Treat. Figures Gram. & Rhetorike f. lxiiv For the Citizens of Rome, both wer thei fraunchisers, and brought out of other countreys, there to enhabite.
But was repurposed in American English to someone who holds a franchise.
1889 Oakland (Calif.) Tribune 2 Dec. 1/2 The apparatus is intended to assist railroad franchisers to turn the corners of streets with their cable cars.
1949 Wall St. Jrnl. 1 Feb. 6/5 Hertz supplies accounting information, helps franchisers set up rate structures and advises them on buying equipment.
Franchisee: 1956 Trademark Reporter 46 45 Opposer adopted the word slim for vitamin-fortified skim milk in 1949 and by use of franchises extended the sale of its products to 40 dairies in 21 states. Mark is normally used in conjunction with the primary mark of the franchisee.
Franchisor 1960 Jrnl. Marketing 25 102/1 The franchisor's activities are largely contained in the establishment of ‘brand recognition’ and in advertising in the areas where franchised outlets operate to establish recognition.
Solution 2:
The definition of a franchiser is a company that {offers} franchise rights to those who want to own a franchise.
The definition of a franchisor is a company which or person who has granted {and governs} a franchise.
So if you are referring to someone (or some company) that offers franchise rights, use franchiser, but if you are referring to the entity that granted franchise rights, use franchisor.
"The ABC company is a franchiser who became the franchisor of John's new company."
For additional sourcing, read Franchisor and Franchiser.