We describe the new project FORCA-G, which aims at studying the short range interactions between a surface and atoms trapped in its vicinity. Using cold atoms confined in the wells of an optical standing wave, the atom-surface potential will be measured with high sensitivity using atom interferometry techniques. The experiment will allow a test of gravity at short distances, which will put stringent bounds on a possible deviation from the known laws of physics. FORCA-G will also allow a measurement of the Casimir Polder interaction (QED vacuum fluctuations) with unprecedented accuracy.