Chlorine has vacant d orbitals hence it can show an oxidation state of +3. Fluorine has no d orbitals, it cannot show positive oxidation state. Fluorine shows only -1 oxidation state. Therefore FCl₃ does not exists.

This can also be explained by the concept of atomic size. Size of chlorine atom is greater due to smaller size of fluorine atom it cannot accommodate three large chlorine atoms.

Hence ClF₃ exists but FCl₃ does not exist.