Would a french drain solve my water issues?
If you have an area to drain the water two that is lower than your crawl space a French drain will work great.
I have seen folks put them in with the drain point higher than the low area they were trying to keep dry.
In some cases if natural drainage is not available a small pit in the drain can be pumped to the storm runoff, this is requires in some areas to prevent standing water under the house.