We investigate analytically the interaction between circular inclusions in smectic-C films with planar anchoring. We present a rigorous solution for an isolated circular colloid with planar anchoring and use it to calculate the interaction between two circular colloids, approximately. At large separations the interaction is quadrupolar and we show that at short range two different regimes may be observed. For weak anchoring, the interaction is always attractive in some directions, which may lead to particle contact or coalescence. However, for strong anchoring, the interaction exhibits a well defined minimum, for colloids at a particular separation and given relative orientation. The equilibrium configuration was found to depend on. the anchoring strength.