The formation of stars has been subject to extensive studies in the past decades on scales from molecular clouds to protoplanetary disks. It is still not fully understood how the surrounding material in a protostellar system, which often shows asymmetric structures with complex kinematic properties, feeds the central protostar(s) and their disk(s). We study the spatial morphology and kinematic properties of the molecular gas surrounding the IRS3A and IRS3B protostellar systems in the L1448N region located in the Perseus molecular cloud. We present 1\,mm Northern Extended Millimeter Array (NOEMA) observations of the large program PROtostars DIsks: Global Evolution (PRODIGE). We analyzed the kinematic properties of molecular lines. Because the spectral profiles are complex, the lines were fit with up to three Gaussian velocity components. The clustering algorithm called density-based spatial clustering of applications with noise ( DBSCAN ) was used to disentangle the velocity components in the underlying physical structure. We discover an extended gas bridge (approx 3000\,au) surrounding both the IRS3A and IRS3B systems in six molecular line tracers (C18O, SO, DCN $CO, HC$_ $N, and CH$_ $ toward the IRS3A system. We find that the observed velocity profile is consistent with analytical streamline models of gravitational infall toward IRS3A. The high-velocity C18O ($2-1$) emission toward IRS3A indicates a protostellar mass of approx 1.2\,$M_ odot$. While high angular resolution continuum data often show IRS3A and IRS3B in isolation, molecular gas observations reveal that these systems are still embedded within a large-scale mass reservoir, whose spatial morphology and velocity profiles are complex. The kinematic properties of the extended gas bridge are consistent with gravitational infall toward the protostar IRS3A.