Pavers in the backyard.. need some help

So I bought a house in NYC last year and the part of the backyard is pavers. I noticed some stains on the pavers (from me, and my bad bad BBQ habits) along with the joints exposed so I was going to do some maintenance on them (powerwash them to clear the shitty weeds out / clear the stains, fill the joints and then seal the pavers). The drainage situation is a little weird which is why I am making this post..

The previous owner stated that there is a french drain located where the pavers are, and is covered by the pavers. We have not had any issues with flooding at all, but would feel much better if we extended the drain (which I think his run off is connected to the sewer, where the grade goes and levels off is where the sewer line is as per the blueprints) and installed a zipper line.

I guess my question is does this make sense to extend the drain to the top of the pavers and what is the best way to do this? I haven't done anything with pavers ever so this is new territory for myself.

TL;DR: drain is covered by pavers. Want to expose and extend the drain to the top.