The effective monitoring of water pollution and further purification are pressing yet challenging issues for guaranteeing the health of human beings and the stabilization of ecological systems. For this purpose, the development of efficient sensing and adsorption materials as a result of supramolecular interactions, including coordination and H-bonding etc., have been attracting increasing attention. With the aid of a coordination-driven self-assembly strategy, a new nonporous 2D Cu^II coordination network, [Cu₂L(H₂O)₂]_n (donated as CuCP), based on H₄L, where H₄L = 4-(4-(3,5-di-carboxy-pyridin-4-yl)phenyl)pyridine-2,6-dicarboxylic acid, was afforded hydrothermally. Structural analysis indicated that CuCP featured a wrinkled network similar to the ancient Chinese folding screens and constructed by the fully deprotonated ligand L⁴⁻ with the coordination mode of bis(μ₂-η¹:η¹:η²) and penta-coordinated Cu²⁺, which could be further upgraded to a supramolecular 3D framework as a result of the synergism of multiple C–H⋯O hydrogen bonds. The hydrostability of CuCP could be maintained within a wide pH range from 2 to 12 as verified by PXRD determination, endowing it with potential environmental applications. Thanks to the combination of the soft Lewis acidity of Cu²⁺ and its large conjugated structure, CuCP could be used as a turn-on fluorescence sensor for S²⁻ and exhibited a different fluorescence response when Na₂S, (NH₄)₂S or H₂S were incorporated, even in actual water samples. The sensing mechanisms were disclosed in detail by the combination of experiments and density functional theory (DFT) calculations. Furthermore, CuCP was shown to be a selective and recoverable adsorbent with a maximum adsorption capacity of 379 mg g⁻¹ in 60 minutes for methylene blue (MB). The adsorption mechanism could be a combination of π⋯π stacking, n⋯π interaction, aggregation effects and Soft and Hard Acid–Base theory (HSAB). The results presented herein open up new perspectives for Cu^II species in environmental applications.