How tall are the fences and is there anything by them that your beagle can get onto? We have a 6 foot vinyl fence and there is no jumping that. Of course if there was a woodpile or small shed up against it, then they might be able to get over. I am always out there with them to supervise too.
As long as the puppy is kept entertained, is trained and is supervised you shouldn't have issues with anything being ruined. Beagles are curious and love to be with the family. My dogs are inside all the time unless I am outside with them, too much trouble 3 can get into without me!! For puppy owners I always suggest a basic manners puppy class.