How would I install hydronic floor heat on top of a rigid foam insulated basement floor?
For a ThermoFin U extruded aluminum heat transfer plate installation on concrete, you would build a surface to be able to screw the plates into by first putting down a layer of Atlas Rboard®, recommended 1/2", which you should be able to get from your local building supplier.
A Google search on Atlas Rboard® will bring up their site and the product info.

On top of the Rboard® put down a layer of plywood. The fasteners will hold best if you can use 3/8" plywood. It will work with 1/2" plywood if necessary.

Keep in mind that you want the heat energy to be going into the sleepers and the finish floor, which is why we recommend the Rboard®.

The energy without the layer of insulation will be drawn into the concrete, and the response time would be longer in heating the floor. Heating up the mass of concrete is not necessarily a good thing when you want the entire surface floor to be warmed. 

Radiant Engineering aka Radiant Design &amp; Supply has decades of success with ThermoFin U and ThermoFin C installations in North America. Install ThermoFin U with the fins facing down for wood finish flooring. For tile or stone, install with the fins facing up. The sandwich of aluminum and plywood provide an evenly heated surface that is friendly to finish flooring installation. ThermoFin U specs are .050" gauge, width 4", length either 4 ft or 8 ft, tubing channel size either nominal 1/2" or 3/8".