This is not something a layman should be messing with. If you have concerns about the placement or functionality of the french drain, call that out to the contractor and suggest that a soils engineer be called in for a consultation. Or hire one yourself.

The plus side is that once the back side of the drain has been planted, you should have far less problem with runoff and soil erosion. Without seeing the property, it's hard to be specific, but I would think this could very easily and attractively transitioned to a more naturalistic planting area, perhaps incorporating some native plantings, both trees and shrubs, as well as smaller ornamental plantings and groundcovers.

French drains are rather common in my area due to the prevalence of sloped lots and issues very similar to those you describe and often define the boundary between lawns and mixed planting areas. Rather than the coarse gravel used for the bulk of the drain system, these are often "finished" with river rock, providing more of a dry stream effect and typically become an accent to the landscape rather than a detraction.

I've been reading a little more about it. Can I cover the french drain with soil and then grass it? Again, it's pretty big - about 130' long and probably 3' wide. That would look good at least. It just is aesthetically ugly.

If I can put grass and sod on it; would that be OK?

I'm assuming that with the hill, and now that the neighbors have grass growing , a lot of the water infiltration is going to be "sub-surface"

You need an engineer. Perhaps the City Engineer from the town that you live in would be helpful.

I would probably not cover the drain with grass until the surrounding area is covered with grass. Eventually the grass will fill in on its own, but to get grass to grow there now might be a mistake. I would probably protect the drain from getting silted in with some silt fence. If the dirt is getting into the drain, eventually it could clog and not work.

One of the most complete sites with discussion of drainage issues in the garden is PavingExpert.com. It is an English site with lots of information on paving, of course, but also about how to determine and install drainage.

Dealing with the water collected by the drain is also another issue. A primary consideration is the soil permiability or whether you have a spot for it to flow out to the surface and on to a stream or neighbor.

However, if properly constructed, it should not be a problem to grass over it. Look at the methods on the site linked below. Even if I were to want to make it look to be a dry streambed, I would want to make sure that the landscape fabric was covering and containing the actual drain portion of the installation so that it will not silt up.

Here is a link that might be useful: Paving Expert Drainage Introduction Page