The CF is not in the business of giving LOANS. CANEX does not give Loans. Canex does allow defered payments, post dated cheques, and assistance in financing purchases, but not Loans. A Service Member can apply for a CFPAT Loan through their Unit Orderly Room, but the hoops one has to go through to get this 'Pay Advance' are usually not worth the effort for the small amount that you would get, and the conditions of returning the funds.
So the answer would be that you will have to go to a Bank or other Financial Lending agency to get a Car Loan. ADVICE - Stay away from Trans Canada Credit or any other such 'Institution'.