Do you mean sump?

I thought the french drain was the cut out of the concrete floor that runs along the perimiter of the basement (it's usually filled in with gravel)? But thats what I am talking about. the sump pumplooks fine.

Both definitions apply.

If it feels dry and smells dry even after heavy rain, it probably is dry.

However, I would be very interested as to why the closed cell board is only on the bottom of the walls. If one was building with insulation only part way, it would normally be at the top, which is above grade. (In fact, that is the Code minimum in our area.)

An interior perimeter drain would only be used in our area as a cure for a water problem, not as part of new construction. When I've built anticipating a water problem I've added interior perimeter drains under the concrete as well as taking other measures.

Here is a link that might be useful: French drains defined