I would like to offer an alternative explanation. The answer provided by J. LS does not provide the main reason for why the $\ce {C-F}$ bond is stronger than the $\ce {C-Cl}$ bond. Yes, it is true that fluorine's $\ce {2p}$ orbital is less diffuse than chlorine's $\ce {3p}$ orbital. However, it is also important to note that orbital energies need to be accounted out in determining the effectiveness of the covalent interaction between two orbitals. In order for two orbitals to interact strongly, they must be of similar sizes and energies. The Pauling electronegativity values of fluorine and chlorine are $\ce {3.98}$ and $\ce {3.16}$ respectively while the value for carbon is $\ce {2.55}$. Clearly, the orbital energies of chlorine and carbon would be more similar than the orbital energies of fluorine and carbon. Thus, we cannot conclude that the covalent interaction between carbon's and fluorine's atomic orbitals is stronger than that between carbon's and chlorine's atomic orbitals.
What then can we use to rationalise the bond strengths?
We can actually explain this using the idea of bond polarity and ionic contributions to the covalent bond. Lemal (2004) reports that the partial charge on carbon in the molecule $\ce {CF4}$ is $\ce {+0.76}$. This illustrates that partial charges are actually very significant when looking at the $\ce {C-F}$ bond. Thus, it is due to this ionic character of the $\ce {C-F}$ bond, that is, the attraction between the partial positive charge on carbon and the partial negative charge on fluorine, that results in the $\ce {C-F}$ bond being significantly stronger than the $\ce {C-Cl}$ bond.
Reference
Lemal, D. M. (2004). Perspective on Fluorocarbon Chemistry. The Journal of Organic Chemistry,69(1), 1-11. doi:10.1021/jo0302556