If an almost product structure $P$ on the tangent space $T(E)=T_V(E)\oplus T_H(E)$ of Lagrangian $2n$ dimensional manifold $E$ is defined, and if $f_v(3,\varepsilon)$-structure on $T_V(E)$ is defined, then $f_h(3,\varepsilon)$-structure on $T_H(E)$ are defined in the natural way. We can define $F(3,\varepsilon)$-structure on $T(E)$. In the Lagrangian $F(3,\varepsilon)$-manifold we have studied two linear connections, defined in [4] in terms of an arbitrary connection, distribution's parallelism and geodesic curve.