Hard to tell from the pic, but those look more like fir or spruce? Needles look too short to be pine.
But anyway, yeah, scratch my insufficient sunlight comment - those don't look to be casting much shade. Looks like you might have some erosion issues there, like some of the topsoil has washed away. That could contribute to grasses having difficulty taking root, especially with the competition from tree roots.
There's various things you could try planting in that area, but by far the easiest would be just to mulch it and call it good. Try taking a string trimmer and scalp as much of the existing grass/weeds as you can without damaging the tree roots, then put down like a 4-5" layer of mulch. Bagged mulch will work if it's all that's available, but remember that it doesn't cover nearly as much as it looks like it will, so buy plenty.