We construct a theory of quantum fluctuations in a regular array of small superconductive islands of size d connected via low-resistance tunnel contacts (Gt=h/4e2Rt≫1) to a dirty thin metal film with dimensionless conductance g≫1. Electrons in the film interact repulsively with the dimensionless strength λ. The system is macroscopically superconductive when the distance b between neighbouring islands is short enough. The zero-temperature phase transition from the superconductive to the normal-conductive state is shown to occur with the increase of distance between superconductive islands, at ln bc/d~Gt2/λg. The critical distance bc is much less than the 2d localization length Lloc~eπg, so the considered effect develops when weak-localization corrections are still small. The Tc(g, b) dependence at b<bc is found. These results are valid at sufficiently large g, whereas a decrease of g is expected to lead eventually to another bc(g) dependence, ln bc/d~g.