Fencers should select shoes that are low to the ground, and offer good lateral stability. This excludes runners and many shoes worn by the casual club fencer. Choosing the right shoe for fencing is important for learning correct movements; they should offer stability and cushioning.
Club coaches ask that beginners bring clean indoor court shoes to training, but which ones will are closest to an actual fencing shoe?
Runners elevate the heel too much, and do not offer nearly enough lateral stability, as the shoe elevates the soul too much above the ground. The toe in runners is elevated off the ground when flat, and are to be avoided.
More info about fencing specific shoes and other options