A vane arc segment includes an airfoil piece that defines a first platform and an airfoil section that extends from the first platform. The first platform defines a radial flange that extends along at least a portion of a circumferential mate face of the first platform. The airfoil piece is formed of a fiber-reinforced composite that has fibers that are continuous between the airfoil section and the first platform. The airfoil section carries a second platform radially opposite the first platform. The second platform includes a through-hole, and the airfoil section extends through the through-hole.