How does the Fama and French 3-factor model explain stock covariance? Does it at all? If so, how?

It is understood that size and value play a role in determining returns and there are proposed explanation those these, but what about covariance?
It is not clear to what covariance this question refers to. 

As in the CAPM model the covariance among assets is reduced to $\beta$, through the covariance with the market index.

$\beta_i=\sigma_{i,M}/\sigma_M^2$

Then, if CAPM is correct, we could explain the covariance relating the $\beta$s

$\sigma_{i,j}=\beta_i*\beta_j*\sigma_M^2$

In the context of multifactor models something similar occurs, since, in order to use those models, it is necessary to estimate $\beta$s, or sensitivities, related to each proposed factors.