Most of the time when a foundation moves it is because the soil under the foundation is moving. Most soil movement is caused by changing water content in the soil. As a result, most foundation movement can be controlled by controlling ground water.
A French drain is a drainage system composed of a trench, containing one or more pipes, with the pipes surrounded by gravel. The gravel may or may not extend to the surface, and the gravel may or may not be wrapped in geotechnical cloth. In a better drainage system, the gravel is wrapped in geotechnical cloth.
Geotechnical cloth is a fabric made of materials, such as fiberglass, that do not decay and that allow water to pass through while preventing soil from passing through. If the gravel in a trench is not wrapped in geotechnical cloth, soil, sand, and clay will fill the gaps between the pieces of gravel, plug up the drain, and cause the drain to stop working. Wrapping the drain line in geotechnical cloth (sometimes call a pipe in a sock) is less effective than wrapping the trench. If dirt plugs up the gravel, water can not get to the drain line, and the drain will plug up, so the lining on the pipe will be useless.
A French drain system is designed to collect water that is flowing or accumulating below the surface. If your problem is poor surface drainage, you should install surface drains. Surface drains are much less costly than French Drains.
When installing a French drain system, it is better to use straight sections of perforated PVC (a white plastic) for the drain lines. Do not use the black corrugated ABS pipe. The corrugated pipe will bend over time as the ground moves. As the pipe becomes uneven, it traps water and debris. ABS pipe is more likely to get plugged up, as the corrugations will catch debris, such as twigs and leaves.
Do not connect your gutters to a French drain system. Filling a French drain with water from gutters will push water into the ground. Remember, the purpose of a French drain is to remove ground water. Connecting your gutters to your French drain system can actually add enough water to the soil to lift your home!