More of an estoc than a rapier. The shield would be more useful if it was like a buckler, held with a center-grip. Fencers and infantrymen armed with a rapier are called rapierists.

What the gentleman below is probably referring to is a smallsword.

Rapiers are usually use for duel purposes, depending on the historical you look em up for, so usually their just duelists arm with rapier. Well done by the well.