"No, thanks, I am full."
Translation:Nej tak, jeg er mæt.
Jens er mæt = Jens has had enough to eat and is no longer hungry.
Jens er fuld = Jens is under the influence of alcohol to the point where his physical and mental abilities are impaired.
(Definitions taken from Den Danske Ordbog for mæt and fuld).
Fuld can also mean an object is physically full or an action that can't have more effect than it already has (for example fuld fart = full speed)