We have investigated the electronic structure of electron-doped Sr$_{2-x}$La$_x$FeMoO$_6$ ($x$=0.0 and 0.2) by photoemission spectroscopy and band-structure calculations within the local-density approximation+$U$ (LDA+$U$) scheme. A characteristic double-peak feature near the Fermi level ($E_{rm F}$) has been observed in the valence-band photoemission spectra of both $x$=0.0 and 0.2 samples. A photon-energy dependence of the spectra in the Mo 4$d$ Cooper minimum region compared with the band-structure calculations has shown that the first peak crossing $E_{rm F}$ consists of the (Fe+Mo) $t_{2gdownarrow}$ states (feature A) and the second peak well below $E_{rm F}$ is dominated by the Fe $e_{guparrow}$ states (feature B). Upon La substitution, the feature A moves away from $E_{rm F}$ by $sim$50 meV which is smaller than the prediction of our band theory, 112 meV. In addition, an intensity enhancement of $both$ A and B has been observed, although B is not crossing $E_{rm F}$. Those two facts are apparently incompatible with the simple rigid-band shift due to electron doping. We point out that such phenomena can be understood in terms of the strong Hunds rule energy stabilization in the 3$d^5$ configuration at the Fe sites in this compound. From an observed band-narrowing, we have also deduced a mass enhancement of $sim$2.5 with respect to the band theory, in good agreement with a specific heat measurement.
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