We have studied effects of the partial substitution of $La^{3+}$ for $A^{2+}$ on the magnetic properties of double perovskites $A_2FeMoO_6$ (A=Ca, Sr and Ba). Polycrystalline $A_{2-x}La_xFeMoO_6(0{leq}x{leq}0.2)$ samples have been prepared by the conventional solid-state reaction in a stream of 5% $H_2$/Ar gas. The x-ray data indicate that A=Ca is monoclinic with the space group P$2_1$/n, A=Sr is tetragonal with the space group I4/mmm, and A=Ba is cubic with the space group Fm3m. The substitution of $La^{3+}$ for $A^{2+}$ results in a cell volume increase for A=Ca and a cell volume reduction for A=Ba. The decrease of saturation magnetization with increasing x arises from the reduction of magnetic moment associated with the electron doping and the disorder at the Fe and Mo sites. The partial substitution of magnetic $La^{3+}$ for $A^{2+}$ considerably enhances the Curie temperature $T_c$ from 316 K for x = 0 to 334 K for x = 0.2. This enhancement of $T_c$ with $La^{3+}$ doping originates from electron doping effects in addition to ionic size ones.