There are many.
On the athletic side, speed and endurance must rank foremost. Other traits that can be exploited are strength (for explosive speed, not heavy-handedness), precision, and flexibility. Quick reaction time is extremely important.
On the intellectual side, a good mind for strategy and tactics is essential. The ability to quickly size up your opponent and adapt your style accordingly is essential.
Psychologically, a fencer must be able to maintain focus, concentration, and emotional level-headedness under intense conditions of combat. Stress management, visualization, and relaxation techniques are all helpful to putting in winning performances.
As far as body type goes, it is always possible to adapt your style to take advantage of your natural traits. Even so, height seems to be useful in epeé, but not necessarily in sabre. Small or thin people are harder to hit in foil. A long reach helps in epeé, and mobility is useful in sabre.