All aspects of the body need to be trained
Fencing is a sport that requires all around athleticism, speed, strength, endurance, flexibility, mental toughness and the list goes on. Most of all is the mental aspect of the game, you want to be able to maximize your physical strengths and ensure your weaknesses are not vulnerable. Your training regimen should be structured specifically to the fencer to achieve those goals.
Training areas I would emphasize:
Plyometrics: Explosive strength, jumping, accelerating
Agility: Balance and coordination
Concentration: Your mental state while exerting yourself is very important to fencing. The warmups we use as a team are geared toward challenging the fencers ability to concentrate.
Training Videos