This article is from the Fencing FAQ, by Morgan Burke with numerous contributions by others.
All of them.
On the athletic side, speed and cardiovascular fitness rank
foremost. Other traits that can be exploited are strength (for
explosive power, not heavy handedness), manual dexterity, and
flexibility. Quick reaction time is extremely important. On the
mental side, a fencer must be adaptable and observant, and have a
good mind for strategy and tactics. Psychologically, he or she
must be able to maintain focus, concentration, and emotional
level-headedness under intense conditions of combat.
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 most useful in epee. Small or thin people are harder
to hit in foil. A long reach helps in epee, and long legs are an
asset in foil.
It should be noted that left handers seem to enjoy a slight
advantage, especially against less experienced fencers. This may
account for the fact that lefties make up 15% of novice fencers,
but close to half of FIE world champions.