I think your suggestion might help but will not likely fix the problem unless it is buried very deep.

The problem is typically that the soil beneath the front porch concrete slab is supported with brackets or knee supports that are part of the foundation of the house. Typically the porch slab stays relatively stable but the soil beneath the slab settles (drops) in the first few years after the home is built. This results in a void, a pocket of air, an open sump for water to flow to and then slowly seep into the soil under the front porch. In the first few years after the house is built, homeowners fill soil around the foundation to grade up the settling soil but cannot place soil under the porch … so the void remains. This is typical and common.

Your drain tile/French drain idea will work if you bury the pipe deep enough to drain the void/pocket/sump area under the slab with a gravity sloped pipe. This is like installing a drain pipe in the bottom of a “bowl” to let the water drain out of the bottom. Packing soil tightly under the concrete can work in theory but is difficult to fill and compact newly added soil under the concrete from the side. Try draining the void from the side if your terrain slopes enough to maintain a pipe slope of at least 1/8″ per foot of run, preferably 1/4″ per foot of pipe length.