French drain lower than sump pump?
Water is either coming up from below (a rising water table) or its coming from surface water (the surrounding ground water in the saturated soil.) Either way, it needs to be collected and carried away. 

IMHO, it’s preferred to collect and deal with the water outside of the basement. 

If it comes up from a rising water table, it will enter the living space from below through cracks between the foundation wall and slab.

If it comes from the surrounding ground water, it COULD enter the living space through the wall, especially if the exterior side of the foundation wall is not sealed properly.
Either way the moisture enters the living space it will need to be collected and disposed. I think the best way to collect it is on the exterior side of the foundation wall in drainrock and a perf pipe laid 6”-8” below the basement slab. 

To keep the subsurface water from seeping through the wall, I recommend installing a moisture barrier on the exterior side of the foundation wall and install a 2” thick plastic mesh on the wall to allow water to flow down to the perf pipe. If dirt is allowed to be backfilled against the wall, the dirt could hold the moisture giving it a chance to seep through the wall.

Once collected it needs to be disposed by extending a solid pipe over an embankment or in a collection well enclosure and pumped away.

IMHO, it’s preferred to collect and dispose of the moisture on the outside of the basement, rather than inside the basement. This will eliminate the possibility of mold inside the basement and eliminate a possible power failure causing the sump pump to fail (even with battery backups) and thus water damage. This may be the most expensive method of solving the problem, but it’s sure to work.

One reason your footings are so much lower than your basement slab is due to the frost line. If so, you may need heat tape on your drain and float switch.