Are you planning on keeping animals in?
If so, you can't cross the property line to attach to their fence to keep your animals in without permission. If they give you permission to attach to their fence, splendid. If not, you'd have to fence your own property.
Some states have laws that require adjoining property owners to share the cost of a fence. If your state is one of those (I don't thing FL is, but you'd have to check) you could force them to pay for half of a fence directly on the property line.
When we bought our first house, we got a puppy. We wanted to fence the yard. I had it surveyed. Part of the neighbors driveway and all of the shared trash can pad in the alley were on my property. His garage was 6" from the property line. If I wanted to, I could have put my fence right on the property line, he'd have never been able to maintain the side of the garage facing my lot, he'd have lost about 5' of driveway apron at the alley, and have to move his trash cans to the other side of the driveway.
Fortunately, we liked them. I explained the situation and that we would fence 3' onto our side of the property line, I didn't care that his trash cans were on a pad on my property, and I'd maintain both sides of the fence, with the understanding that they wouldn't attach to my fence if they ever fenced the yard. Easy peasy and thank goodness for good neighbors.