We have searched for first generation scalar leptoquark (LQ) pairs in the $e\ensuremath{\nu}+\mathrm{jets}$ channel using $p\overline{p}$ collider data $(\ensuremath{\int}L\mathrm{dt}\ensuremath{\approx}115{\mathrm{pb}}^{\ensuremath{-}1})$ collected by the D0 experiment at the Fermilab Tevatron during 1992--1996. The analysis yields no candidate events. We combine the results with those from the $ee+\mathrm{jets}$ and $\ensuremath{\nu}\ensuremath{\nu}+\mathrm{jets}$ channels to obtain 95% confidence level (C.L.) upper limits on the LQ pair production cross section as a function of mass and of $\ensuremath{\beta}$, the branching fraction to a charged lepton. Comparing with the next-to-leading order theory, we set 95% C.L. lower limits on the LQ mass of 225, 204, and $79\mathrm{GeV}{/c}^{2}$ for $\ensuremath{\beta}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1$, $\frac{1}{2}$, and 0, respectively.