The resolution of data acquired over modern seafloors does not allow imaging of the inner features of a fluid seep structure, particularly in the shallow subsurface. In the SE Basin of France (Drôme), fossil cold seep structures comprising fossil-rich carbonate lenses were identified about 30 years ago within the Oxfordian (Late Jurassic) Terres Noires Formation. These structures were first interpreted as pseudo-bioherms related to hydrothermal activity, but comparison with active seep sites on modern margins, together with isotopic analyses, led to a reinterpretation involving cold fluids instead. To date, all seep sites have generally been studied individually without considering any link to neighbouring or more distant sites. Based on 23 high-resolution stratigraphic logs within the structure coupled to mosaicked aerial photographs from a drone survey, 19 fluid seep events were correlated in the area, including two new sites exposed as a result of weathering. We have shown that each identified sub-site is composed of subvertically stacked fossil-rich carbonate lenses interbedded with marls, which developed in smooth, 4-6 m deep depressions beneath the local seabed. The nodules present within the depressions are of primary importance as they mark the area of active seeping. This general organization is very similar to the modern Regab giant pockmark in the Lower Congo Basin where only a few sub-sites are active at the same time. A spatio-temporal 3D reconstruction of the position of these sub-sites shows that the carbonate lenses are organized into clusters comprising up to seven sub-sites grouped together in the same stratigraphic interval and the same geographical zone. A sandbox experiment where gas is injected at constant flow rate at the base of a box filled with a matrix of water-saturated grains displays a pattern consisting of disturbed sediments inside a parabolic-shaped area. This parabolic shape was also identified on a seismic profile across the Regab giant pockmark, suggesting that the processes are similar for the Beauvoisin and Regab seep areas. The laboratory experiments also show that the seeping conduit is stable during a given period of time and suddenly shifts laterally. This is mainly as a result of the collapse of the conduit, the lateral migration and the reopening at a new position. The general log obtained in the Beauvoisin seep area suggests a similar pattern with periods of seeping alternating with periods of quiescence, each of which is c. 200 kyr. Even if a pockmark seems to have been inactive for a long period of time, this could be due to the lateral shift of the feeder conduit, meaning that the sub-seafloor is still charged with gas. This is of primary importance for risk assessment, hydrocarbon exploration and general understanding of geobiology at seafloor seeps.