Since the septic system and drainfield are below the level of the floor drain, the backup indicates that the water level in the drainfield is about the same level as the floor drain, and thus higher after rains. If you dig into your drainfield, you should find the water levels high. You can pump your septic tank, but it basically does not give you more than a few days of drainage in the drainfild before it starts to fill up again. 

Septic Scub(TM) drainfield flow restorer can help situations such as yours. By dissolving the black sludge and other anaerobic by-products, flow can be restored to the field. 

You should dig a post hole in the drainfield to determine the water levels. This will help you to understand what to do. Please give me a call at (888) 352-7226 to discuss your situation further.