We study Andreev reflection in a ballistic one-dimensional channel coupled in parallel to a superconductor via a tunnel barrier of finite length L. The dependence of the low-energy Andreev reflection probability R-A on L reveals the existence of a characteristic length scale xi(N) beyond which R-A(L) is enhanced up to unity despite the low interfacial transparency. The Andreev reflection enhancement is due to the strong mixing of particle and hole states that builds up in contacts exceeding the coherence length xi(N), leading to a small energy gap (minigap) in the density of states of the normal system. The role of the geometry of such hybrid contacts is discussed in the context of the experimental observation of zero-bias Andreev anomalies in the resistance of extended carbon nanotube/superconductor junctions in field effect transistor setups.