You also need to check out your local codes. The towns where I live do not allow sump pumps for groundwater to discharge into the sewer systems due to system overload during storms. You should have a separate discharge line running outside well away from the foundation of your house, just as you would do for a gutter downspout.
The sewage lines and pumps for a basement bathroom would be totally separate, and require a pump that can either handle solids or a macerating unit to chop up the solids before they go through the pump.
Even if your codes don't require the groundwater to discharge separately, it is still a good idea so that if anything goes wrong with your sewage system in you basement bathroom you don't have a bunch of groundwater from the french drains flooding it.