Not only will you need a refinance, you'll need to transfer title and registration to yourself as well. All of this will require the fiance's signatures and cooperation.
Right now, with him as the primary, the car is titled to him with a first lien to Honda Financial. Other than being a guarantor (cosigner) on the note, you have no ownership of the vehicle. For you to move with it to California and re-register it there, you will need to have your name on it. It matters not who made the payments, it's whose name is on the paperwork as primary - that's the person the vehicle is titled to.
What you're technically looking to do is not really a refi in the strictest sense - you're actually trying to buy it from your cosigner, and that involves paying off Honda Financial so they will release the title to the new lender. You'll also have to file a title transfer in Florida to get your name on it and his off.
The good news is, you have a good score and should have no trouble getting financing from a number of lenders.
Since title work is invovled beyond what would be required with a regular refi, you might actually want to consider going the trade-in route - assuming of course that your fiance will cooperate with going into the dealer to sign the title over. Technically you are a first-time buyer, and you also have a Tier-1 credit score, so you should be able to get a good rate and some incentives for buying new (or used, even) with a dealer. Then the dealer will unravel the title issues on the old car and title the new one to you alone - meaning you won't have to worry about making sure that gets done right, like you would if you decided to go the sort-of-refi route.
