I hope others chime in here. Here are my thoughts. If your underground drainage system was to be in trenches, then directing collected water to a pumping facility, then your use of fabric and sand sounds like it will work, but I'd revise the drainage trench detail to simplify it and save costs. Laying those materials in water will not be easy. Pumping from open trenches can loosen the soil there and result in settlements later when loads are placed on the trench areas. I'd look at a procedure for materials and installing the sub-drains as follows:
Immediately in back of the excavator lower in a drainage pipe consisting of flexible corrugated plastic, with small slots, perhaps 2 or 3 mm and wrappped with a filter fabric sock. As soon as possible then backfill over that pipe, sufficient thickness to "bury" the pipe. The backfill over and around the pipe should be a graded sand , such as ASTM C-33 fine aggregate for concrete. DO NOT USE THE COARSE AGGREGATE FOR CONCRETE, SINCE IT IS NOT A FILTER. This filter zone could be in the range of 15 cm or more depth. Later use what ever soil came from the trench to get up to finish grade.
If you have to work in an already dug trench, lowering the water level a little with pumping can be done, but not so extensive as to remove all water and cause loosening of the soil below the trench. I'd try to work without any pumping.
That ASTM-C33 concrete coarse fine aggregate sand is a perfect filter for all soils. You do not need any filter fabric in the trench first. Even a slotted pipe without a filter sock will work, but a little sand gets in first and then bridges over the slots. Since the pipe is not fully surrounded with soil, the dumping on top of it will likely surround it sufficiently. A fussy way would be to place the sand in a thin layer first and then the pipe, but that takes time and may not be practical.
Size the pipe to carry the estimated flow. In the States, I'd use 4 inch for lengths of up to 100 meters, and 6" for all others. Here these flexible pipes come in rolls for ease of handling. I'd not get too fussy about meeting a sloping grade under the circumstances you have. So some low areas result, so what. It will still work.