Someone may correct me but I think some of the alarm systems have some sort of backup battery? So perhaps the car last remembers being alarmed, you've then gained entry to the car with the actual key and introduced some power to the battery resulting in the alarm?
To stop the horn sound I would try: pressing the unlock button on your fob. Failing that, pressing it rapidly several times in a row. Failing that, sticking the key in and turning the ignition on.
Again someone may correct me
but if the battery is that weak it may need some charging before the above works.