Why do you need to level it?

Measure the width of the french drain opening and get styrofoam the same thickness, cut into needed height strips and stick it in there and level the floor, after you are done leveling the floor get the styrofoam out.

btydrvn, because it's not level and want to finish basement.

You need an entirely different moisture management system if you’re going to finish the basement. Are the exterior walls actually waterproofed? Start there. Prevent the water from getting in, and having to be handled by internal means.

Basments aren't supposed to be level. The concrete is laid so if there is any water that enters the basement it will flow to the drain.

The french was put in (about 5 years ago) after the house was built. The house was built in 1950.

It is really more complicated than we think….how cold will it be down there?…can you incorporate any natural light ..it can feel like a dungeon with no natural light or air…if you get any moisture mold can follow..sleeping there could be a health hazard

An exit window is also a good idea

There are 3 windows and a bilco door. It's gets down to about the low 60s

If its leaky enough to need an internal drain, its a poor candidate for finishing. You will need to stop the water at the exterior plane to change that.

I thought there was a way to level the floor without going over the area where the french drain and sump pump are.

I think so too…with the other additional info it seems doable…but the concrete contractor should be chosen with care as they will make the decisions on how to finish your project…be sure they are reputable and insured