French Drain with rubber mulch?
I assume you are talking about this.

I have seen this product used twice before in this type of application.I have never used it in a french drain, however, I packed some into the end of a downspout so the water wouldn't drill a hole into the ground.

I have also seen it used as a substitute for rock in a drainage ditch along the outside wall of a house. Months later they wound that the rubber was compacting under its own weight and the weight of the dirt above it and began to lose its functionality and actually prevented water from leaving the area. The surface area is too great along lateral edges,(it lays flat) so it begins to clog up.

I assume that your question steams from worrying about the difference between rock and rubber. In your case I would NOT use the rubber because the rubber mulch could settle in the drain and block up the pipe, especially if the mulch is longer than it is wider. I'd use rock. It won't bend or flex, plus it's proven.