We study the proximity coherence in a mesoscopic normal-metal film in conta
ct with a superconductor. Accounting for a repulsive interaction between th
e electrons in the normal metal, we find an enhanced local density of state
s close to the normal-metal-superconductor intel face. The sharp peak in th
e density is pinned to the Fermi energy and leads to spontaneous paramagnet
ic interface currents. The induced orbital magnetic moments exhibit the cha
racteristic features of the paramagnetic reentrance observed in normal-meta
l coated superconducting cylinders [P. Visani, A.C. Mota, and A. Pollini, P
hys. Rev. Lett. 65, 1514 (1990)]. [S0031-9007(99)08939-5].